Deck 13: Inference About Comparing Two Populat

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When comparing two population variances, we use the ratio When comparing two population variances, we use the ratio   rather than the difference   .<div style=padding-top: 35px> rather than the difference When comparing two population variances, we use the ratio   rather than the difference   .<div style=padding-top: 35px> .
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Question
The test statistic employed to test The test statistic employed to test   is   is F -distributed with v <sub>1</sub> = n <sub>1</sub> - 1 and v <sub>2</sub> = n <sub>2</sub> - 1 degrees of freedom if the two populations are F -distributed.<div style=padding-top: 35px> is The test statistic employed to test   is   is F -distributed with v <sub>1</sub> = n <sub>1</sub> - 1 and v <sub>2</sub> = n <sub>2</sub> - 1 degrees of freedom if the two populations are F -distributed.<div style=padding-top: 35px> is F -distributed with v 1 = n 1 - 1 and v 2 = n 2 - 1 degrees of freedom if the two populations are F -distributed.
Question
The F -test used for testing the difference in 2 population variances is always a one-tailed test.
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In constructing a confidence interval estimate for the difference between two population proportions, we pool the population proportions when the populations are normally distributed.
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When the necessary conditions are met, a two-tail test is being conducted at a = 0.05 to test When the necessary conditions are met, a two-tail test is being conducted at a = 0.05 to test   . The two sample variances are   and   , and the sample sizes are n <sub>1</sub> = 25 and n <sub>2</sub> = 25. The calculated value of the test statistic will be F = 2.<div style=padding-top: 35px> . The two sample variances are When the necessary conditions are met, a two-tail test is being conducted at a = 0.05 to test   . The two sample variances are   and   , and the sample sizes are n <sub>1</sub> = 25 and n <sub>2</sub> = 25. The calculated value of the test statistic will be F = 2.<div style=padding-top: 35px> and When the necessary conditions are met, a two-tail test is being conducted at a = 0.05 to test   . The two sample variances are   and   , and the sample sizes are n <sub>1</sub> = 25 and n <sub>2</sub> = 25. The calculated value of the test statistic will be F = 2.<div style=padding-top: 35px> , and the sample sizes are n 1 = 25 and n 2 = 25. The calculated value of the test statistic will be F = 2.
Question
A required condition for using the normal approximation to the binomial in testing the difference between two population proportions is that n 1 p 1 ³ 30 and n 2 p 2 ³ 30.
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The pooled proportion estimate is used when the proportion of successes from sample 1 equals the proportion of successes from sample 2.
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In testing for the equality of two population variances, when the populations are normally distributed, the 5% level of significance has been used. To determine the rejection region, it will be necessary to refer to the F table corresponding to an upper-tail area of 0.05.
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The F -distribution is symmetric.
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When testing the equality of two population variances the number in the null hypothesis is 0.
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We use a t -test to determine whether two population variances are equal.
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The pooled proportion estimate is found by taking the proportion of successes from sample 1 plus the proportion of successes from sample 2.
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The pooled proportion estimate is used when the null hypothesis states that the two population proportions differ by some non-zero number.
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The F -distribution can only have non-negative values.
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Pooling is made possible by hypothesizing (under the null hypothesis)that p 1 = p 2.
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The expected value of the difference between two sample proportions is the difference between their corresponding population proportions.
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All F -tests for the equality of two population variances are one-tailed tests.
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The test for the equality of two population variances assumes that each of the two populations is normally distributed.
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The difference in two sample proportions is an unbiased consistent estimator of the difference in their respective population proportions.
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In comparing two population means the statistic under consideration is In comparing two population means the statistic under consideration is   .<div style=padding-top: 35px> .
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When testing for the difference between two population variances with sample sizes of n 1 = 8 and n 2 = 10, the degrees of freedom are:

A)8 and 10
B)7 and 9
C)2 and 18
D)18 and 2
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The variance of the difference in sample proportions equals the difference of their population variances.
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Which of the following statements is false for an F- distribution?

A)Variables that are F -distributed range from 0 to ¥ .
B)The exact shape of the distribution is determined by two numbers of degrees of freedom.
C)The degrees of freedom for the numerator can be larger than, smaller than, or equal to the degrees of freedom for the denominator.
D)All of these choices are true.
Question
In testing for the equality of two population variances, when the populations are normally distributed, the 10% level of significance has been used. To determine the rejection region, it will be necessary to refer to the F table corresponding to an upper-tail area of:

A)0.90
B)0.20
C)0.10
D)0.05
Question
For testing the difference between two population proportions, the pooled proportion estimate is found by taking:

A)the proportion of successes from sample 1 plus the proportion of successes from sample 2.
B)the total number of successes in both samples divided by the total of both sample sizes.
C)the difference between the proportion of successes in each sample.
D)None of these choices.
Question
Which of the following statements is correct regarding the percentile points of the F- distribution?

A)F 0.05,10,20 = 1\ F 0.95,10,20
B)F 0.05,10,20 = 1\ F 0.05,20,10
C)F 0.95,10,20 = 1\ F 0.05,20,10
D)F 0.95,10,20 = 1\ F 0.95,20,10
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Two independent samples are drawn from two normal populations, where the population variances are assumed to be equal. The sampling distribution of the ratio of the two sample variances is:

A)normal
B)Student- t
C)F
D)chi-squared
Question
The pooled proportion estimate is used when:

A)the proportion of successes from sample 1 equals the proportion of successes from sample 2.
B)the total number of successes in both samples divided by the total of both sample sizes equals 1.
C)the null hypothesis states that the two population proportions differ by some non-zero number.
D)None of these choices.
Question
The sampling distribution of the ratio of two sample variances <strong>The sampling distribution of the ratio of two sample variances   is said to be F -distributed provided that:</strong> A)the samples are independent from any distributions. B)the populations are normal with equal variances. C)the samples are matched and their sizes are large. D)the samples are independently drawn from two normal populations. <div style=padding-top: 35px> is said to be F -distributed provided that:

A)the samples are independent from any distributions.
B)the populations are normal with equal variances.
C)the samples are matched and their sizes are large.
D)the samples are independently drawn from two normal populations.
Question
The sampling distribution of the ratio of two sample variances is said to be F -distributed provided that we have two ____________________ samples drawn from their respective populations.
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The ratio of two independent chi-squared variables divided by their degrees of freedom is:

A)normally distributed
B)Student t -distributed
C)chi-squared distributed
D)F- distributed
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The sampling distribution of the ratio of two (independent)sample variances is said to be ____________________ distributed.
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In constructing a confidence interval estimate for the difference between two population proportions, we:

A)pool the population proportions when the populations are normally distributed.
B)pool the population proportions when the population means are equal.
C)pool the population proportions when they are equal.
D)never pool the population proportions.
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The F- distribution is the sampling distribution of the ratio of:

A)two sample variances.
B)two normal population means.
C)two normal population variances.
D)None of these choices.
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To estimate the ratio of the population variances you use the ____________________ of the ____________________ variances.
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The test statistic for testing for the equality of two population variances has a(n)____________________ distribution.
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For testing the difference between two population proportions, the pooled proportion estimate should be used to compute the value of the test statistic when the:

A)populations are normally distributed.
B)sample sizes are small.
C)null hypothesis states that the two population proportions are equal.
D)samples are independently drawn from the populations.
Question
The statistical distribution used for testing the difference between two population variances is the

A)Student t -distribution
B)standard normal distribution
C)F -distribution
D)None of these choices.
Question
Which of the following is a required condition for using the normal approximation to the binomial in testing the difference between two population proportions?

A) <strong>Which of the following is a required condition for using the normal approximation to the binomial in testing the difference between two population proportions?</strong> A)   B)   ,   ,   , and   C)   ,   ,   , and   D)Choice b is the true requirement, but choice c is the one you actually check. <div style=padding-top: 35px>
B) <strong>Which of the following is a required condition for using the normal approximation to the binomial in testing the difference between two population proportions?</strong> A)   B)   ,   ,   , and   C)   ,   ,   , and   D)Choice b is the true requirement, but choice c is the one you actually check. <div style=padding-top: 35px> , <strong>Which of the following is a required condition for using the normal approximation to the binomial in testing the difference between two population proportions?</strong> A)   B)   ,   ,   , and   C)   ,   ,   , and   D)Choice b is the true requirement, but choice c is the one you actually check. <div style=padding-top: 35px> , <strong>Which of the following is a required condition for using the normal approximation to the binomial in testing the difference between two population proportions?</strong> A)   B)   ,   ,   , and   C)   ,   ,   , and   D)Choice b is the true requirement, but choice c is the one you actually check. <div style=padding-top: 35px> , and <strong>Which of the following is a required condition for using the normal approximation to the binomial in testing the difference between two population proportions?</strong> A)   B)   ,   ,   , and   C)   ,   ,   , and   D)Choice b is the true requirement, but choice c is the one you actually check. <div style=padding-top: 35px>
C) <strong>Which of the following is a required condition for using the normal approximation to the binomial in testing the difference between two population proportions?</strong> A)   B)   ,   ,   , and   C)   ,   ,   , and   D)Choice b is the true requirement, but choice c is the one you actually check. <div style=padding-top: 35px> , <strong>Which of the following is a required condition for using the normal approximation to the binomial in testing the difference between two population proportions?</strong> A)   B)   ,   ,   , and   C)   ,   ,   , and   D)Choice b is the true requirement, but choice c is the one you actually check. <div style=padding-top: 35px> , <strong>Which of the following is a required condition for using the normal approximation to the binomial in testing the difference between two population proportions?</strong> A)   B)   ,   ,   , and   C)   ,   ,   , and   D)Choice b is the true requirement, but choice c is the one you actually check. <div style=padding-top: 35px> , and <strong>Which of the following is a required condition for using the normal approximation to the binomial in testing the difference between two population proportions?</strong> A)   B)   ,   ,   , and   C)   ,   ,   , and   D)Choice b is the true requirement, but choice c is the one you actually check. <div style=padding-top: 35px>
D)Choice b is the true requirement, but choice c is the one you actually check.
Question
The test for the equality of two population variances is based on the:

A)difference between the two sample variances.
B)ratio of the two sample variances.
C)sum of the two sample variances.
D)product of the two sample variances.
Question
The difference in two sample proportions is a(n)____________________ estimator of the difference in their respective population proportions.
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The expected value of the difference between two sample proportions is the ____________________ of\between their corresponding population proportions.
Question
Profit Margin An investor is considering two types of investment. She is quite satisfied that the expected profit margin on Investment 1 is higher than the expected profit margin on Investment 2. However, she is quite concerned that the risk associated with Investment 1 is higher than that of Investment 2. To help make her decision, she randomly selects seven monthly profit margins on investment 1 and ten monthly profit margins on investment 2. She finds that the sample variances of Investments 1 and 2 are 225 and 118, respectively. {Profit Margin Narrative} Can she infer at the 5% significance level that the population variance of investment 1 exceeds that of investment 2?
Question
If the sample sizes are large enough so the conditions are met, the difference between two sample proportions has an approximate ____________________ distribution.
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Random samples from two normal populations produced the following statistics: Random samples from two normal populations produced the following statistics:   ,   ,   , and   . Is there enough evidence at the 5% significance level to infer that the variance of Population 1 is larger than the variance of Population 2?<div style=padding-top: 35px> , Random samples from two normal populations produced the following statistics:   ,   ,   , and   . Is there enough evidence at the 5% significance level to infer that the variance of Population 1 is larger than the variance of Population 2?<div style=padding-top: 35px> , Random samples from two normal populations produced the following statistics:   ,   ,   , and   . Is there enough evidence at the 5% significance level to infer that the variance of Population 1 is larger than the variance of Population 2?<div style=padding-top: 35px> , and Random samples from two normal populations produced the following statistics:   ,   ,   , and   . Is there enough evidence at the 5% significance level to infer that the variance of Population 1 is larger than the variance of Population 2?<div style=padding-top: 35px> . Is there enough evidence at the 5% significance level to infer that the variance of Population 1 is larger than the variance of Population 2?
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In constructing a confidence interval estimate for the difference between two population proportions, we ____________________ (always\sometimes\never)pool the population proportions.
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When the data from two populations are ____________________ the parameter to be tested and estimated is the difference between the two population proportions.
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We compare two population variances by examining their ____________________.
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Clinic Waiting Time In a random sample of 20 patients who visited a clinic at Medical Center 1, a researcher found that the variance of the waiting time (in minutes)was 128.0. In a random sample of 15 patients in the clinic of Medical Center 2, the researcher found the variance to be 178.8. {Clinic Waiting Time Narrative} Can we infer at the 5% level of significance that the population variances differ?
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The pooled proportion estimate is used when the null hypothesis states that the two population proportions differ by ____________________.
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The variance of the difference between two sample proportions equals the ____________________ of their population proportion variances.
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Fitness Program A statistician wants to test for the equality of means in two independent samples drawn from normal populations of people enrolled in a fitness program. However, he will not perform the equal-variance t -test of the difference between the population means if the condition necessary for its use is not satisfied. The number of pound lost at the completion of the program data follow: Fitness Program A statistician wants to test for the equality of means in two independent samples drawn from normal populations of people enrolled in a fitness program. However, he will not perform the equal-variance t -test of the difference between the population means if the condition necessary for its use is not satisfied. The number of pound lost at the completion of the program data follow:   {Fitness Program Narrative} Can the statistician conclude at the 5% significance level that the required condition is not satisfied?<div style=padding-top: 35px> {Fitness Program Narrative} Can the statistician conclude at the 5% significance level that the required condition is not satisfied?
Question
When testing for the equality of two population variances the number in the null hypothesis is ____________________.
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The test statistic for testing for the equality of two population variances has an F -distribution with ____________________ and ____________________ degrees of freedom.
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If the F -test statistic is large, that means the variance of Population 1 is ____________________ than\to the variance of Population 2.
Question
Profit Margin An investor is considering two types of investment. She is quite satisfied that the expected profit margin on Investment 1 is higher than the expected profit margin on Investment 2. However, she is quite concerned that the risk associated with Investment 1 is higher than that of Investment 2. To help make her decision, she randomly selects seven monthly profit margins on investment 1 and ten monthly profit margins on investment 2. She finds that the sample variances of Investments 1 and 2 are 225 and 118, respectively. {Profit Margin Narrative} Estimate with 95% confidence the ratio of the two population variances.
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In constructing a confidence interval estimate for the difference between two population proportions, we ____________________ (always\sometimes\never)pool the population proportions.
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Pooling is made possible by hypothesizing (under the null hypothesis)that p 1 __________ p 2.
Question
Fitness Program A statistician wants to test for the equality of means in two independent samples drawn from normal populations of people enrolled in a fitness program. However, he will not perform the equal-variance t -test of the difference between the population means if the condition necessary for its use is not satisfied. The number of pound lost at the completion of the program data follow: Fitness Program A statistician wants to test for the equality of means in two independent samples drawn from normal populations of people enrolled in a fitness program. However, he will not perform the equal-variance t -test of the difference between the population means if the condition necessary for its use is not satisfied. The number of pound lost at the completion of the program data follow:   {Fitness Program Narrative} Estimate with 95% confidence the ratio of the two population variances and interpret.<div style=padding-top: 35px> {Fitness Program Narrative} Estimate with 95% confidence the ratio of the two population variances and interpret.
Question
Profit Margin An investor is considering two types of investment. She is quite satisfied that the expected profit margin on Investment 1 is higher than the expected profit margin on Investment 2. However, she is quite concerned that the risk associated with Investment 1 is higher than that of Investment 2. To help make her decision, she randomly selects seven monthly profit margins on investment 1 and ten monthly profit margins on investment 2. She finds that the sample variances of Investments 1 and 2 are 225 and 118, respectively. {Profit Margin Narrative} Briefly describe what the interval estimate tells you.
Question
Headache Medicine A researcher wants to see if\how men and women differ in their reaction to a headache medicine with respect to drowsiness. In testing the hypotheses Headache Medicine A researcher wants to see if\how men and women differ in their reaction to a headache medicine with respect to drowsiness. In testing the hypotheses   vs.   , the following statistics were obtained: n <sub>1</sub> = 400, x <sub>1</sub> = 208, n <sub>2</sub> = 250, and x <sub>2</sub> = 115, where x <sub>1</sub> and x <sub>2</sub> represent the number of patients in the two samples (men vs. women)who reported to have drowsiness as a result of taking headache medicine. {Headache Medicine Narrative} Estimate with 90% confidence the difference between the two population proportions.<div style=padding-top: 35px> vs. Headache Medicine A researcher wants to see if\how men and women differ in their reaction to a headache medicine with respect to drowsiness. In testing the hypotheses   vs.   , the following statistics were obtained: n <sub>1</sub> = 400, x <sub>1</sub> = 208, n <sub>2</sub> = 250, and x <sub>2</sub> = 115, where x <sub>1</sub> and x <sub>2</sub> represent the number of patients in the two samples (men vs. women)who reported to have drowsiness as a result of taking headache medicine. {Headache Medicine Narrative} Estimate with 90% confidence the difference between the two population proportions.<div style=padding-top: 35px> , the following statistics were obtained: n 1 = 400, x 1 = 208, n 2 = 250, and x 2 = 115, where x 1 and x 2 represent the number of patients in the two samples (men vs. women)who reported to have drowsiness as a result of taking headache medicine. {Headache Medicine Narrative} Estimate with 90% confidence the difference between the two population proportions.
Question
Antioxidants A food processor wants to compare two antioxidants for their effects on retarding spoilage. Suppose 16 cuts of fresh meat are treated with antioxidant A and 16 are treated with antioxidant B, and the number of hours until spoilage begins is recorded for each of the 32 cuts of meat. The results are summarized in the table below Antioxidants A food processor wants to compare two antioxidants for their effects on retarding spoilage. Suppose 16 cuts of fresh meat are treated with antioxidant A and 16 are treated with antioxidant B, and the number of hours until spoilage begins is recorded for each of the 32 cuts of meat. The results are summarized in the table below   {Antioxidants Narrative} Develop the 95% confidence interval estimate of the ratio of the two population variances.<div style=padding-top: 35px> {Antioxidants Narrative} Develop the 95% confidence interval estimate of the ratio of the two population variances.
Question
Antioxidants A food processor wants to compare two antioxidants for their effects on retarding spoilage. Suppose 16 cuts of fresh meat are treated with antioxidant A and 16 are treated with antioxidant B, and the number of hours until spoilage begins is recorded for each of the 32 cuts of meat. The results are summarized in the table below Antioxidants A food processor wants to compare two antioxidants for their effects on retarding spoilage. Suppose 16 cuts of fresh meat are treated with antioxidant A and 16 are treated with antioxidant B, and the number of hours until spoilage begins is recorded for each of the 32 cuts of meat. The results are summarized in the table below   {Antioxidants Narrative} Explain how to use the 95% confidence interval for testing the equality of the two population variances at the 5% level.<div style=padding-top: 35px> {Antioxidants Narrative} Explain how to use the 95% confidence interval for testing the equality of the two population variances at the 5% level.
Question
TV Sex A survey of 1,500 Canadians reveals that 945 believe that there is too much sex on television. In a survey of 1,500 Americans, 810 believe that there is too much television sex. {TV Sex Narrative} Estimate with 99% confidence the difference in the proportion of Canadians and Americans who believe that there is too much sex on television.
Question
TV Sex A survey of 1,500 Canadians reveals that 945 believe that there is too much sex on television. In a survey of 1,500 Americans, 810 believe that there is too much television sex. {TV Sex Narrative} Briefly explain what the interval estimate tells you.
Question
TV Sex A survey of 1,500 Canadians reveals that 945 believe that there is too much sex on television. In a survey of 1,500 Americans, 810 believe that there is too much television sex. {TV Sex Narrative} Can we infer at the 99% significance level that the proportion of Canadians and Americans who believe that there is too much sex on television differ?
Question
Antioxidants A food processor wants to compare two antioxidants for their effects on retarding spoilage. Suppose 16 cuts of fresh meat are treated with antioxidant A and 16 are treated with antioxidant B, and the number of hours until spoilage begins is recorded for each of the 32 cuts of meat. The results are summarized in the table below Antioxidants A food processor wants to compare two antioxidants for their effects on retarding spoilage. Suppose 16 cuts of fresh meat are treated with antioxidant A and 16 are treated with antioxidant B, and the number of hours until spoilage begins is recorded for each of the 32 cuts of meat. The results are summarized in the table below   {Antioxidants Narrative} Calculate the value of the test statistic for testing the equality of the population variances, and write the proper conclusion.<div style=padding-top: 35px> {Antioxidants Narrative} Calculate the value of the test statistic for testing the equality of the population variances, and write the proper conclusion.
Question
Mass Production Line A quality control examiner keeps a tally sheet of the number of acceptable and unacceptable products that come off two different production lines. The completed sheet is shown below. Mass Production Line A quality control examiner keeps a tally sheet of the number of acceptable and unacceptable products that come off two different production lines. The completed sheet is shown below.   {Mass Production Line Narrative} Estimate with 95% confidence the difference in population proportions.<div style=padding-top: 35px> {Mass Production Line Narrative} Estimate with 95% confidence the difference in population proportions.
Question
Senatorial Election A political poll immediately prior to a senatorial election reveals that 145 out of 250 male voters and 105 out of 200 female voters intend to vote for the Democrat candidate. {Senatorial Election Narrative} Explain how to use the interval estimate to test the hypotheses.
Question
Antioxidants A food processor wants to compare two antioxidants for their effects on retarding spoilage. Suppose 16 cuts of fresh meat are treated with antioxidant A and 16 are treated with antioxidant B, and the number of hours until spoilage begins is recorded for each of the 32 cuts of meat. The results are summarized in the table below Antioxidants A food processor wants to compare two antioxidants for their effects on retarding spoilage. Suppose 16 cuts of fresh meat are treated with antioxidant A and 16 are treated with antioxidant B, and the number of hours until spoilage begins is recorded for each of the 32 cuts of meat. The results are summarized in the table below   {Antioxidants Narrative} Determine the rejection region for testing the equality of the two population variances at a = 0.05.<div style=padding-top: 35px> {Antioxidants Narrative} Determine the rejection region for testing the equality of the two population variances at a = 0.05.
Question
Mass Production Line A quality control examiner keeps a tally sheet of the number of acceptable and unacceptable products that come off two different production lines. The completed sheet is shown below. Mass Production Line A quality control examiner keeps a tally sheet of the number of acceptable and unacceptable products that come off two different production lines. The completed sheet is shown below.   {Mass Production Line Narrative} Can the inspector infer at the 5% significance level that production line 1 is doing a better job than production line 2?<div style=padding-top: 35px> {Mass Production Line Narrative} Can the inspector infer at the 5% significance level that production line 1 is doing a better job than production line 2?
Question
Senatorial Election A political poll immediately prior to a senatorial election reveals that 145 out of 250 male voters and 105 out of 200 female voters intend to vote for the Democrat candidate. {Senatorial Election Narrative} Estimate with 95% confidence the difference in the proportion of male and female voters who intend to vote for the Democrat candidate.
Question
Antioxidants A food processor wants to compare two antioxidants for their effects on retarding spoilage. Suppose 16 cuts of fresh meat are treated with antioxidant A and 16 are treated with antioxidant B, and the number of hours until spoilage begins is recorded for each of the 32 cuts of meat. The results are summarized in the table below
  Antioxidants A food processor wants to compare two antioxidants for their effects on retarding spoilage. Suppose 16 cuts of fresh meat are treated with antioxidant A and 16 are treated with antioxidant B, and the number of hours until spoilage begins is recorded for each of the 32 cuts of meat. The results are summarized in the table below     {Antioxidants Narrative} State the null and alternative hypotheses for determining if the population variances differ for Antioxidants A and B.<div style=padding-top: 35px> {Antioxidants Narrative} State the null and alternative hypotheses for determining if the population variances differ for Antioxidants A and B.
Question
Senatorial Election A political poll immediately prior to a senatorial election reveals that 145 out of 250 male voters and 105 out of 200 female voters intend to vote for the Democrat candidate. {Senatorial Election Narrative} Can we infer at the 5% significance level that the proportions of male and female voters who intend to vote for the Democrat candidate differ?
Question
Mass Production Line A quality control examiner keeps a tally sheet of the number of acceptable and unacceptable products that come off two different production lines. The completed sheet is shown below. Mass Production Line A quality control examiner keeps a tally sheet of the number of acceptable and unacceptable products that come off two different production lines. The completed sheet is shown below.   {Mass Production Line Narrative} What is the p -value of the test? Explain how to use it for testing the hypotheses.<div style=padding-top: 35px> {Mass Production Line Narrative} What is the p -value of the test? Explain how to use it for testing the hypotheses.
Question
Clinic Waiting Time In a random sample of 20 patients who visited a clinic at Medical Center 1, a researcher found that the variance of the waiting time (in minutes)was 128.0. In a random sample of 15 patients in the clinic of Medical Center 2, the researcher found the variance to be 178.8. {Clinic Waiting Time Narrative} Estimate with 95% confidence the ratio of the two population variances and interpret.
Question
A councilwoman regularly polls her constituency to gauge her level of support among voters. This month, 652 out of 1158 voters support her. Five months ago, 412 out of 982 voters supported her. With a 5% significance level, can she infer that support has increased by at least 10 percentage points?
Question
Senatorial Election A political poll immediately prior to a senatorial election reveals that 145 out of 250 male voters and 105 out of 200 female voters intend to vote for the Democrat candidate. {Senatorial Election Narrative} What is the p -value of the test?
Question
Headache Medicine A researcher wants to see if\how men and women differ in their reaction to a headache medicine with respect to drowsiness. In testing the hypotheses Headache Medicine A researcher wants to see if\how men and women differ in their reaction to a headache medicine with respect to drowsiness. In testing the hypotheses   vs.   , the following statistics were obtained: n <sub>1</sub> = 400, x <sub>1</sub> = 208, n <sub>2</sub> = 250, and x <sub>2</sub> = 115, where x <sub>1</sub> and x <sub>2</sub> represent the number of patients in the two samples (men vs. women)who reported to have drowsiness as a result of taking headache medicine. {Headache Medicine Narrative} What conclusion can we draw at the 10% significance level?<div style=padding-top: 35px> vs. Headache Medicine A researcher wants to see if\how men and women differ in their reaction to a headache medicine with respect to drowsiness. In testing the hypotheses   vs.   , the following statistics were obtained: n <sub>1</sub> = 400, x <sub>1</sub> = 208, n <sub>2</sub> = 250, and x <sub>2</sub> = 115, where x <sub>1</sub> and x <sub>2</sub> represent the number of patients in the two samples (men vs. women)who reported to have drowsiness as a result of taking headache medicine. {Headache Medicine Narrative} What conclusion can we draw at the 10% significance level?<div style=padding-top: 35px> , the following statistics were obtained: n 1 = 400, x 1 = 208, n 2 = 250, and x 2 = 115, where x 1 and x 2 represent the number of patients in the two samples (men vs. women)who reported to have drowsiness as a result of taking headache medicine. {Headache Medicine Narrative} What conclusion can we draw at the 10% significance level?
Question
Worker Safety An OSHA agent wanted to determine if efforts to promote safety have been successful. By checking the records of 250 workers, he found that 30 of them suffered either minor or major injuries that year. A random sample of 400 workers last year revealed that 80 suffered some form of injury. {Worker Safety Narrative} Can the statistician infer at the 5% significance level that efforts to promote safety have been successful?
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Deck 13: Inference About Comparing Two Populat
1
When comparing two population variances, we use the ratio When comparing two population variances, we use the ratio   rather than the difference   . rather than the difference When comparing two population variances, we use the ratio   rather than the difference   . .
True
2
The test statistic employed to test The test statistic employed to test   is   is F -distributed with v <sub>1</sub> = n <sub>1</sub> - 1 and v <sub>2</sub> = n <sub>2</sub> - 1 degrees of freedom if the two populations are F -distributed. is The test statistic employed to test   is   is F -distributed with v <sub>1</sub> = n <sub>1</sub> - 1 and v <sub>2</sub> = n <sub>2</sub> - 1 degrees of freedom if the two populations are F -distributed. is F -distributed with v 1 = n 1 - 1 and v 2 = n 2 - 1 degrees of freedom if the two populations are F -distributed.
False
3
The F -test used for testing the difference in 2 population variances is always a one-tailed test.
False
4
In constructing a confidence interval estimate for the difference between two population proportions, we pool the population proportions when the populations are normally distributed.
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5
When the necessary conditions are met, a two-tail test is being conducted at a = 0.05 to test When the necessary conditions are met, a two-tail test is being conducted at a = 0.05 to test   . The two sample variances are   and   , and the sample sizes are n <sub>1</sub> = 25 and n <sub>2</sub> = 25. The calculated value of the test statistic will be F = 2. . The two sample variances are When the necessary conditions are met, a two-tail test is being conducted at a = 0.05 to test   . The two sample variances are   and   , and the sample sizes are n <sub>1</sub> = 25 and n <sub>2</sub> = 25. The calculated value of the test statistic will be F = 2. and When the necessary conditions are met, a two-tail test is being conducted at a = 0.05 to test   . The two sample variances are   and   , and the sample sizes are n <sub>1</sub> = 25 and n <sub>2</sub> = 25. The calculated value of the test statistic will be F = 2. , and the sample sizes are n 1 = 25 and n 2 = 25. The calculated value of the test statistic will be F = 2.
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6
A required condition for using the normal approximation to the binomial in testing the difference between two population proportions is that n 1 p 1 ³ 30 and n 2 p 2 ³ 30.
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7
The pooled proportion estimate is used when the proportion of successes from sample 1 equals the proportion of successes from sample 2.
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8
In testing for the equality of two population variances, when the populations are normally distributed, the 5% level of significance has been used. To determine the rejection region, it will be necessary to refer to the F table corresponding to an upper-tail area of 0.05.
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9
The F -distribution is symmetric.
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10
When testing the equality of two population variances the number in the null hypothesis is 0.
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11
We use a t -test to determine whether two population variances are equal.
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12
The pooled proportion estimate is found by taking the proportion of successes from sample 1 plus the proportion of successes from sample 2.
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13
The pooled proportion estimate is used when the null hypothesis states that the two population proportions differ by some non-zero number.
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14
The F -distribution can only have non-negative values.
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15
Pooling is made possible by hypothesizing (under the null hypothesis)that p 1 = p 2.
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16
The expected value of the difference between two sample proportions is the difference between their corresponding population proportions.
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17
All F -tests for the equality of two population variances are one-tailed tests.
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18
The test for the equality of two population variances assumes that each of the two populations is normally distributed.
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19
The difference in two sample proportions is an unbiased consistent estimator of the difference in their respective population proportions.
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20
In comparing two population means the statistic under consideration is In comparing two population means the statistic under consideration is   . .
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21
When testing for the difference between two population variances with sample sizes of n 1 = 8 and n 2 = 10, the degrees of freedom are:

A)8 and 10
B)7 and 9
C)2 and 18
D)18 and 2
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22
The variance of the difference in sample proportions equals the difference of their population variances.
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23
Which of the following statements is false for an F- distribution?

A)Variables that are F -distributed range from 0 to ¥ .
B)The exact shape of the distribution is determined by two numbers of degrees of freedom.
C)The degrees of freedom for the numerator can be larger than, smaller than, or equal to the degrees of freedom for the denominator.
D)All of these choices are true.
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24
In testing for the equality of two population variances, when the populations are normally distributed, the 10% level of significance has been used. To determine the rejection region, it will be necessary to refer to the F table corresponding to an upper-tail area of:

A)0.90
B)0.20
C)0.10
D)0.05
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25
For testing the difference between two population proportions, the pooled proportion estimate is found by taking:

A)the proportion of successes from sample 1 plus the proportion of successes from sample 2.
B)the total number of successes in both samples divided by the total of both sample sizes.
C)the difference between the proportion of successes in each sample.
D)None of these choices.
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26
Which of the following statements is correct regarding the percentile points of the F- distribution?

A)F 0.05,10,20 = 1\ F 0.95,10,20
B)F 0.05,10,20 = 1\ F 0.05,20,10
C)F 0.95,10,20 = 1\ F 0.05,20,10
D)F 0.95,10,20 = 1\ F 0.95,20,10
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27
Two independent samples are drawn from two normal populations, where the population variances are assumed to be equal. The sampling distribution of the ratio of the two sample variances is:

A)normal
B)Student- t
C)F
D)chi-squared
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28
The pooled proportion estimate is used when:

A)the proportion of successes from sample 1 equals the proportion of successes from sample 2.
B)the total number of successes in both samples divided by the total of both sample sizes equals 1.
C)the null hypothesis states that the two population proportions differ by some non-zero number.
D)None of these choices.
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29
The sampling distribution of the ratio of two sample variances <strong>The sampling distribution of the ratio of two sample variances   is said to be F -distributed provided that:</strong> A)the samples are independent from any distributions. B)the populations are normal with equal variances. C)the samples are matched and their sizes are large. D)the samples are independently drawn from two normal populations. is said to be F -distributed provided that:

A)the samples are independent from any distributions.
B)the populations are normal with equal variances.
C)the samples are matched and their sizes are large.
D)the samples are independently drawn from two normal populations.
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30
The sampling distribution of the ratio of two sample variances is said to be F -distributed provided that we have two ____________________ samples drawn from their respective populations.
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31
The ratio of two independent chi-squared variables divided by their degrees of freedom is:

A)normally distributed
B)Student t -distributed
C)chi-squared distributed
D)F- distributed
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32
The sampling distribution of the ratio of two (independent)sample variances is said to be ____________________ distributed.
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33
In constructing a confidence interval estimate for the difference between two population proportions, we:

A)pool the population proportions when the populations are normally distributed.
B)pool the population proportions when the population means are equal.
C)pool the population proportions when they are equal.
D)never pool the population proportions.
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34
The F- distribution is the sampling distribution of the ratio of:

A)two sample variances.
B)two normal population means.
C)two normal population variances.
D)None of these choices.
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35
To estimate the ratio of the population variances you use the ____________________ of the ____________________ variances.
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36
The test statistic for testing for the equality of two population variances has a(n)____________________ distribution.
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37
For testing the difference between two population proportions, the pooled proportion estimate should be used to compute the value of the test statistic when the:

A)populations are normally distributed.
B)sample sizes are small.
C)null hypothesis states that the two population proportions are equal.
D)samples are independently drawn from the populations.
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38
The statistical distribution used for testing the difference between two population variances is the

A)Student t -distribution
B)standard normal distribution
C)F -distribution
D)None of these choices.
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39
Which of the following is a required condition for using the normal approximation to the binomial in testing the difference between two population proportions?

A) <strong>Which of the following is a required condition for using the normal approximation to the binomial in testing the difference between two population proportions?</strong> A)   B)   ,   ,   , and   C)   ,   ,   , and   D)Choice b is the true requirement, but choice c is the one you actually check.
B) <strong>Which of the following is a required condition for using the normal approximation to the binomial in testing the difference between two population proportions?</strong> A)   B)   ,   ,   , and   C)   ,   ,   , and   D)Choice b is the true requirement, but choice c is the one you actually check. , <strong>Which of the following is a required condition for using the normal approximation to the binomial in testing the difference between two population proportions?</strong> A)   B)   ,   ,   , and   C)   ,   ,   , and   D)Choice b is the true requirement, but choice c is the one you actually check. , <strong>Which of the following is a required condition for using the normal approximation to the binomial in testing the difference between two population proportions?</strong> A)   B)   ,   ,   , and   C)   ,   ,   , and   D)Choice b is the true requirement, but choice c is the one you actually check. , and <strong>Which of the following is a required condition for using the normal approximation to the binomial in testing the difference between two population proportions?</strong> A)   B)   ,   ,   , and   C)   ,   ,   , and   D)Choice b is the true requirement, but choice c is the one you actually check.
C) <strong>Which of the following is a required condition for using the normal approximation to the binomial in testing the difference between two population proportions?</strong> A)   B)   ,   ,   , and   C)   ,   ,   , and   D)Choice b is the true requirement, but choice c is the one you actually check. , <strong>Which of the following is a required condition for using the normal approximation to the binomial in testing the difference between two population proportions?</strong> A)   B)   ,   ,   , and   C)   ,   ,   , and   D)Choice b is the true requirement, but choice c is the one you actually check. , <strong>Which of the following is a required condition for using the normal approximation to the binomial in testing the difference between two population proportions?</strong> A)   B)   ,   ,   , and   C)   ,   ,   , and   D)Choice b is the true requirement, but choice c is the one you actually check. , and <strong>Which of the following is a required condition for using the normal approximation to the binomial in testing the difference between two population proportions?</strong> A)   B)   ,   ,   , and   C)   ,   ,   , and   D)Choice b is the true requirement, but choice c is the one you actually check.
D)Choice b is the true requirement, but choice c is the one you actually check.
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40
The test for the equality of two population variances is based on the:

A)difference between the two sample variances.
B)ratio of the two sample variances.
C)sum of the two sample variances.
D)product of the two sample variances.
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41
The difference in two sample proportions is a(n)____________________ estimator of the difference in their respective population proportions.
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42
The expected value of the difference between two sample proportions is the ____________________ of\between their corresponding population proportions.
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43
Profit Margin An investor is considering two types of investment. She is quite satisfied that the expected profit margin on Investment 1 is higher than the expected profit margin on Investment 2. However, she is quite concerned that the risk associated with Investment 1 is higher than that of Investment 2. To help make her decision, she randomly selects seven monthly profit margins on investment 1 and ten monthly profit margins on investment 2. She finds that the sample variances of Investments 1 and 2 are 225 and 118, respectively. {Profit Margin Narrative} Can she infer at the 5% significance level that the population variance of investment 1 exceeds that of investment 2?
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44
If the sample sizes are large enough so the conditions are met, the difference between two sample proportions has an approximate ____________________ distribution.
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45
Random samples from two normal populations produced the following statistics: Random samples from two normal populations produced the following statistics:   ,   ,   , and   . Is there enough evidence at the 5% significance level to infer that the variance of Population 1 is larger than the variance of Population 2? , Random samples from two normal populations produced the following statistics:   ,   ,   , and   . Is there enough evidence at the 5% significance level to infer that the variance of Population 1 is larger than the variance of Population 2? , Random samples from two normal populations produced the following statistics:   ,   ,   , and   . Is there enough evidence at the 5% significance level to infer that the variance of Population 1 is larger than the variance of Population 2? , and Random samples from two normal populations produced the following statistics:   ,   ,   , and   . Is there enough evidence at the 5% significance level to infer that the variance of Population 1 is larger than the variance of Population 2? . Is there enough evidence at the 5% significance level to infer that the variance of Population 1 is larger than the variance of Population 2?
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46
In constructing a confidence interval estimate for the difference between two population proportions, we ____________________ (always\sometimes\never)pool the population proportions.
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47
When the data from two populations are ____________________ the parameter to be tested and estimated is the difference between the two population proportions.
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48
We compare two population variances by examining their ____________________.
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49
Clinic Waiting Time In a random sample of 20 patients who visited a clinic at Medical Center 1, a researcher found that the variance of the waiting time (in minutes)was 128.0. In a random sample of 15 patients in the clinic of Medical Center 2, the researcher found the variance to be 178.8. {Clinic Waiting Time Narrative} Can we infer at the 5% level of significance that the population variances differ?
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50
The pooled proportion estimate is used when the null hypothesis states that the two population proportions differ by ____________________.
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51
The variance of the difference between two sample proportions equals the ____________________ of their population proportion variances.
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52
Fitness Program A statistician wants to test for the equality of means in two independent samples drawn from normal populations of people enrolled in a fitness program. However, he will not perform the equal-variance t -test of the difference between the population means if the condition necessary for its use is not satisfied. The number of pound lost at the completion of the program data follow: Fitness Program A statistician wants to test for the equality of means in two independent samples drawn from normal populations of people enrolled in a fitness program. However, he will not perform the equal-variance t -test of the difference between the population means if the condition necessary for its use is not satisfied. The number of pound lost at the completion of the program data follow:   {Fitness Program Narrative} Can the statistician conclude at the 5% significance level that the required condition is not satisfied? {Fitness Program Narrative} Can the statistician conclude at the 5% significance level that the required condition is not satisfied?
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53
When testing for the equality of two population variances the number in the null hypothesis is ____________________.
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54
The test statistic for testing for the equality of two population variances has an F -distribution with ____________________ and ____________________ degrees of freedom.
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55
If the F -test statistic is large, that means the variance of Population 1 is ____________________ than\to the variance of Population 2.
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56
Profit Margin An investor is considering two types of investment. She is quite satisfied that the expected profit margin on Investment 1 is higher than the expected profit margin on Investment 2. However, she is quite concerned that the risk associated with Investment 1 is higher than that of Investment 2. To help make her decision, she randomly selects seven monthly profit margins on investment 1 and ten monthly profit margins on investment 2. She finds that the sample variances of Investments 1 and 2 are 225 and 118, respectively. {Profit Margin Narrative} Estimate with 95% confidence the ratio of the two population variances.
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57
In constructing a confidence interval estimate for the difference between two population proportions, we ____________________ (always\sometimes\never)pool the population proportions.
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58
Pooling is made possible by hypothesizing (under the null hypothesis)that p 1 __________ p 2.
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59
Fitness Program A statistician wants to test for the equality of means in two independent samples drawn from normal populations of people enrolled in a fitness program. However, he will not perform the equal-variance t -test of the difference between the population means if the condition necessary for its use is not satisfied. The number of pound lost at the completion of the program data follow: Fitness Program A statistician wants to test for the equality of means in two independent samples drawn from normal populations of people enrolled in a fitness program. However, he will not perform the equal-variance t -test of the difference between the population means if the condition necessary for its use is not satisfied. The number of pound lost at the completion of the program data follow:   {Fitness Program Narrative} Estimate with 95% confidence the ratio of the two population variances and interpret. {Fitness Program Narrative} Estimate with 95% confidence the ratio of the two population variances and interpret.
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60
Profit Margin An investor is considering two types of investment. She is quite satisfied that the expected profit margin on Investment 1 is higher than the expected profit margin on Investment 2. However, she is quite concerned that the risk associated with Investment 1 is higher than that of Investment 2. To help make her decision, she randomly selects seven monthly profit margins on investment 1 and ten monthly profit margins on investment 2. She finds that the sample variances of Investments 1 and 2 are 225 and 118, respectively. {Profit Margin Narrative} Briefly describe what the interval estimate tells you.
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61
Headache Medicine A researcher wants to see if\how men and women differ in their reaction to a headache medicine with respect to drowsiness. In testing the hypotheses Headache Medicine A researcher wants to see if\how men and women differ in their reaction to a headache medicine with respect to drowsiness. In testing the hypotheses   vs.   , the following statistics were obtained: n <sub>1</sub> = 400, x <sub>1</sub> = 208, n <sub>2</sub> = 250, and x <sub>2</sub> = 115, where x <sub>1</sub> and x <sub>2</sub> represent the number of patients in the two samples (men vs. women)who reported to have drowsiness as a result of taking headache medicine. {Headache Medicine Narrative} Estimate with 90% confidence the difference between the two population proportions. vs. Headache Medicine A researcher wants to see if\how men and women differ in their reaction to a headache medicine with respect to drowsiness. In testing the hypotheses   vs.   , the following statistics were obtained: n <sub>1</sub> = 400, x <sub>1</sub> = 208, n <sub>2</sub> = 250, and x <sub>2</sub> = 115, where x <sub>1</sub> and x <sub>2</sub> represent the number of patients in the two samples (men vs. women)who reported to have drowsiness as a result of taking headache medicine. {Headache Medicine Narrative} Estimate with 90% confidence the difference between the two population proportions. , the following statistics were obtained: n 1 = 400, x 1 = 208, n 2 = 250, and x 2 = 115, where x 1 and x 2 represent the number of patients in the two samples (men vs. women)who reported to have drowsiness as a result of taking headache medicine. {Headache Medicine Narrative} Estimate with 90% confidence the difference between the two population proportions.
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62
Antioxidants A food processor wants to compare two antioxidants for their effects on retarding spoilage. Suppose 16 cuts of fresh meat are treated with antioxidant A and 16 are treated with antioxidant B, and the number of hours until spoilage begins is recorded for each of the 32 cuts of meat. The results are summarized in the table below Antioxidants A food processor wants to compare two antioxidants for their effects on retarding spoilage. Suppose 16 cuts of fresh meat are treated with antioxidant A and 16 are treated with antioxidant B, and the number of hours until spoilage begins is recorded for each of the 32 cuts of meat. The results are summarized in the table below   {Antioxidants Narrative} Develop the 95% confidence interval estimate of the ratio of the two population variances. {Antioxidants Narrative} Develop the 95% confidence interval estimate of the ratio of the two population variances.
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63
Antioxidants A food processor wants to compare two antioxidants for their effects on retarding spoilage. Suppose 16 cuts of fresh meat are treated with antioxidant A and 16 are treated with antioxidant B, and the number of hours until spoilage begins is recorded for each of the 32 cuts of meat. The results are summarized in the table below Antioxidants A food processor wants to compare two antioxidants for their effects on retarding spoilage. Suppose 16 cuts of fresh meat are treated with antioxidant A and 16 are treated with antioxidant B, and the number of hours until spoilage begins is recorded for each of the 32 cuts of meat. The results are summarized in the table below   {Antioxidants Narrative} Explain how to use the 95% confidence interval for testing the equality of the two population variances at the 5% level. {Antioxidants Narrative} Explain how to use the 95% confidence interval for testing the equality of the two population variances at the 5% level.
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64
TV Sex A survey of 1,500 Canadians reveals that 945 believe that there is too much sex on television. In a survey of 1,500 Americans, 810 believe that there is too much television sex. {TV Sex Narrative} Estimate with 99% confidence the difference in the proportion of Canadians and Americans who believe that there is too much sex on television.
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65
TV Sex A survey of 1,500 Canadians reveals that 945 believe that there is too much sex on television. In a survey of 1,500 Americans, 810 believe that there is too much television sex. {TV Sex Narrative} Briefly explain what the interval estimate tells you.
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66
TV Sex A survey of 1,500 Canadians reveals that 945 believe that there is too much sex on television. In a survey of 1,500 Americans, 810 believe that there is too much television sex. {TV Sex Narrative} Can we infer at the 99% significance level that the proportion of Canadians and Americans who believe that there is too much sex on television differ?
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67
Antioxidants A food processor wants to compare two antioxidants for their effects on retarding spoilage. Suppose 16 cuts of fresh meat are treated with antioxidant A and 16 are treated with antioxidant B, and the number of hours until spoilage begins is recorded for each of the 32 cuts of meat. The results are summarized in the table below Antioxidants A food processor wants to compare two antioxidants for their effects on retarding spoilage. Suppose 16 cuts of fresh meat are treated with antioxidant A and 16 are treated with antioxidant B, and the number of hours until spoilage begins is recorded for each of the 32 cuts of meat. The results are summarized in the table below   {Antioxidants Narrative} Calculate the value of the test statistic for testing the equality of the population variances, and write the proper conclusion. {Antioxidants Narrative} Calculate the value of the test statistic for testing the equality of the population variances, and write the proper conclusion.
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68
Mass Production Line A quality control examiner keeps a tally sheet of the number of acceptable and unacceptable products that come off two different production lines. The completed sheet is shown below. Mass Production Line A quality control examiner keeps a tally sheet of the number of acceptable and unacceptable products that come off two different production lines. The completed sheet is shown below.   {Mass Production Line Narrative} Estimate with 95% confidence the difference in population proportions. {Mass Production Line Narrative} Estimate with 95% confidence the difference in population proportions.
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69
Senatorial Election A political poll immediately prior to a senatorial election reveals that 145 out of 250 male voters and 105 out of 200 female voters intend to vote for the Democrat candidate. {Senatorial Election Narrative} Explain how to use the interval estimate to test the hypotheses.
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70
Antioxidants A food processor wants to compare two antioxidants for their effects on retarding spoilage. Suppose 16 cuts of fresh meat are treated with antioxidant A and 16 are treated with antioxidant B, and the number of hours until spoilage begins is recorded for each of the 32 cuts of meat. The results are summarized in the table below Antioxidants A food processor wants to compare two antioxidants for their effects on retarding spoilage. Suppose 16 cuts of fresh meat are treated with antioxidant A and 16 are treated with antioxidant B, and the number of hours until spoilage begins is recorded for each of the 32 cuts of meat. The results are summarized in the table below   {Antioxidants Narrative} Determine the rejection region for testing the equality of the two population variances at a = 0.05. {Antioxidants Narrative} Determine the rejection region for testing the equality of the two population variances at a = 0.05.
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71
Mass Production Line A quality control examiner keeps a tally sheet of the number of acceptable and unacceptable products that come off two different production lines. The completed sheet is shown below. Mass Production Line A quality control examiner keeps a tally sheet of the number of acceptable and unacceptable products that come off two different production lines. The completed sheet is shown below.   {Mass Production Line Narrative} Can the inspector infer at the 5% significance level that production line 1 is doing a better job than production line 2? {Mass Production Line Narrative} Can the inspector infer at the 5% significance level that production line 1 is doing a better job than production line 2?
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72
Senatorial Election A political poll immediately prior to a senatorial election reveals that 145 out of 250 male voters and 105 out of 200 female voters intend to vote for the Democrat candidate. {Senatorial Election Narrative} Estimate with 95% confidence the difference in the proportion of male and female voters who intend to vote for the Democrat candidate.
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73
Antioxidants A food processor wants to compare two antioxidants for their effects on retarding spoilage. Suppose 16 cuts of fresh meat are treated with antioxidant A and 16 are treated with antioxidant B, and the number of hours until spoilage begins is recorded for each of the 32 cuts of meat. The results are summarized in the table below
  Antioxidants A food processor wants to compare two antioxidants for their effects on retarding spoilage. Suppose 16 cuts of fresh meat are treated with antioxidant A and 16 are treated with antioxidant B, and the number of hours until spoilage begins is recorded for each of the 32 cuts of meat. The results are summarized in the table below     {Antioxidants Narrative} State the null and alternative hypotheses for determining if the population variances differ for Antioxidants A and B. {Antioxidants Narrative} State the null and alternative hypotheses for determining if the population variances differ for Antioxidants A and B.
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74
Senatorial Election A political poll immediately prior to a senatorial election reveals that 145 out of 250 male voters and 105 out of 200 female voters intend to vote for the Democrat candidate. {Senatorial Election Narrative} Can we infer at the 5% significance level that the proportions of male and female voters who intend to vote for the Democrat candidate differ?
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75
Mass Production Line A quality control examiner keeps a tally sheet of the number of acceptable and unacceptable products that come off two different production lines. The completed sheet is shown below. Mass Production Line A quality control examiner keeps a tally sheet of the number of acceptable and unacceptable products that come off two different production lines. The completed sheet is shown below.   {Mass Production Line Narrative} What is the p -value of the test? Explain how to use it for testing the hypotheses. {Mass Production Line Narrative} What is the p -value of the test? Explain how to use it for testing the hypotheses.
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76
Clinic Waiting Time In a random sample of 20 patients who visited a clinic at Medical Center 1, a researcher found that the variance of the waiting time (in minutes)was 128.0. In a random sample of 15 patients in the clinic of Medical Center 2, the researcher found the variance to be 178.8. {Clinic Waiting Time Narrative} Estimate with 95% confidence the ratio of the two population variances and interpret.
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77
A councilwoman regularly polls her constituency to gauge her level of support among voters. This month, 652 out of 1158 voters support her. Five months ago, 412 out of 982 voters supported her. With a 5% significance level, can she infer that support has increased by at least 10 percentage points?
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78
Senatorial Election A political poll immediately prior to a senatorial election reveals that 145 out of 250 male voters and 105 out of 200 female voters intend to vote for the Democrat candidate. {Senatorial Election Narrative} What is the p -value of the test?
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79
Headache Medicine A researcher wants to see if\how men and women differ in their reaction to a headache medicine with respect to drowsiness. In testing the hypotheses Headache Medicine A researcher wants to see if\how men and women differ in their reaction to a headache medicine with respect to drowsiness. In testing the hypotheses   vs.   , the following statistics were obtained: n <sub>1</sub> = 400, x <sub>1</sub> = 208, n <sub>2</sub> = 250, and x <sub>2</sub> = 115, where x <sub>1</sub> and x <sub>2</sub> represent the number of patients in the two samples (men vs. women)who reported to have drowsiness as a result of taking headache medicine. {Headache Medicine Narrative} What conclusion can we draw at the 10% significance level? vs. Headache Medicine A researcher wants to see if\how men and women differ in their reaction to a headache medicine with respect to drowsiness. In testing the hypotheses   vs.   , the following statistics were obtained: n <sub>1</sub> = 400, x <sub>1</sub> = 208, n <sub>2</sub> = 250, and x <sub>2</sub> = 115, where x <sub>1</sub> and x <sub>2</sub> represent the number of patients in the two samples (men vs. women)who reported to have drowsiness as a result of taking headache medicine. {Headache Medicine Narrative} What conclusion can we draw at the 10% significance level? , the following statistics were obtained: n 1 = 400, x 1 = 208, n 2 = 250, and x 2 = 115, where x 1 and x 2 represent the number of patients in the two samples (men vs. women)who reported to have drowsiness as a result of taking headache medicine. {Headache Medicine Narrative} What conclusion can we draw at the 10% significance level?
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80
Worker Safety An OSHA agent wanted to determine if efforts to promote safety have been successful. By checking the records of 250 workers, he found that 30 of them suffered either minor or major injuries that year. A random sample of 400 workers last year revealed that 80 suffered some form of injury. {Worker Safety Narrative} Can the statistician infer at the 5% significance level that efforts to promote safety have been successful?
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Unlock Deck
Unlock for access to all 85 flashcards in this deck.