Question 1

The statistic ( n - 1)s ² \ s ² has a chi-squared distribution with n - 1 degrees of freedom if: A)the sample has a Student t -distribution with degrees of freedom equal to n - 1. B)the sample is normally distributed with variance equal to s ². C)the population is normally distributed with variance equal to s ². D)All of these choices are true.

Accepted Answer

The statistic $(n - 1)s^2 / \sigma^2$ follows a chi-squared distribution with $n - 1$ degrees of freedom if the population from which the sample is drawn is normally distributed with variance equal to $\sigma^2$. This is a fundamental result in statistics related to the properties of the sample variance in a normally distributed population. Choices A and B do not directly relate to the conditions under which the given statistic follows a chi-squared distribution.

Question 2

Based on sample data, the 90% confidence interval limits for the population mean are LCL = 170.86 and UCL = 195.42. If the 10% level of significance were used in testing the hypotheses H ₀: m = 201 vs. H ₁: m ¹ 201, the null hypothesis: A)would be rejected. B)would be accepted. C)would fail to be rejected. D)would become H ₀: m ¹ 201

Accepted Answer

The null hypothesis would be rejected because the hypothesized mean (201) is not within the 90% confidence interval (170.86, 195.42).

Question 3

A robust estimator is one that is:
A)unbiased and symmetrical about zero.
B)consistent and is also mound-shaped.
C)efficient and less spread out.
D)not sensitive to moderate nonnormality.

Accepted Answer

A robust estimator is one that is not sensitive to moderate nonnormality. This means that even if the data is not perfectly normally distributed, the estimator will still provide accurate results. The other choices are not necessarily indicative of a robust estimator.

Question 4

The t -test for a population mean is ____________________, meaning that if the population is nonnormal, the results of the test and confidence interval are still valid as long as the nonnormality is not extreme.

Accepted Answer

The answer of The t -test for a population mean...

Question 5

When the population standard deviation is unknown and the population is normal, the test statistic for testing hypotheses about m is the ____________________- distribution with ____________________ degrees of freedom.

Accepted Answer

The answer of When the population standard deviation is unknown...

Question 6

A major electronics store chain is interested in estimating the average amount its credit card customers spent on their first visit to the chain's new store in the mall. Fifteen credit card accounts were randomly sampled and analyzed with the following results: = $50.50 and s ² = 400. A 95% confidence interval for the average amount the credit card customers spent on their first visit to the chain's new store in the mall is: A)$50.50 ± $9.09. B)$50.50 ± $10.12. C)$50.50 ± $11.08. D)None of these choices.

Accepted Answer

The answer of A major electronics store chain is interested...

Question 7

For statistical inference about the mean of a single population when the population standard deviation is unknown, the degrees for freedom for the t- distribution equal n - 1 because we lose one degree of freedom by using the:
A)sample mean as an estimate of the population mean.
B)sample standard deviation as an estimate of the population standard deviation.
C)sample proportion as an estimate of the population proportion.
D)sample size as an estimate of the population size.

Accepted Answer

When we estimate the population mean using the sample mean, we use one degree of freedom. Therefore, we lose one degree of freedom and the degrees of freedom for the t-distribution is equal to n-1.

Question 8

Researchers determined that 60 Puffs tissues is the average number of tissues used during a cold. Suppose a random sample of 100 Puffs users yielded the following data on the number of tissues used during a cold: = 52 and s = 22. Suppose the test statistic does not fall in the rejection region at a = 0.05. Which of the following conclusions is correct? A)At a = 0.05, we do not reject H ₀. B)At a = 0.05, we reject H ₀. C)At a = 0.05, we accept H ₀. D)Both a and c.

Accepted Answer

The answer of Researchers determined that 60 Puffs tissues is...

Question 9

A random sample of size 15 taken from a normally distributed population revealed a sample mean of 75 and a sample variance of 25. The upper limit of a 95% confidence interval for the population mean would equal:
A)77.77
B)72.23
C)88.85
D)77.27

Accepted Answer

The answer of A random sample of size 15 taken...

Question 10

When the population standard deviation is ____________________ and the population is normal, the test statistic for testing hypotheses about m is the t -distribution with n - 1 degrees of freedom.

Accepted Answer

The answer of When the population standard deviation is ____________________...

Question 11

When the population standard deviation is unknown and the population is ____________________, the test statistic for testing hypotheses about m is the t -distribution with n - 1 degrees of freedom.

Accepted Answer

The answer of When the population standard deviation is unknown...

Question 12

Researchers determined that 60 Puffs tissues is the average number of tissues used during a cold. Suppose a random sample of 100 Puffs users yielded the following data on the number of tissues used during a cold: = 52 and s = 22. Suppose the alternative we wanted to test was H ₁: m a = 0.05 is: A)reject H ₀ if t > 1.6604. B)reject H ₀ if t - 1.6604. C)reject H ₀ if t > 1.9842 or Z - 1.9842. D)reject H ₀ if t - 1.9842.

Accepted Answer

The answer of Researchers determined that 60 Puffs tissues is...

Question 13

Which of the following conditions is needed regarding the chi-squared test statistic for the test of variance?
A)The population random variable must be normal.
B)The test statistic must be a non-negative number.
C)The test statistic must have a chi-squared distribution with n - 1 degrees of freedom.
D)All of these choices are true.

Accepted Answer

All of these conditions are needed for the chi-squared test statistic for the test of variance. 
A) The population random variable does not need to be normal for the chi-squared test of variance.
B) The test statistic must be non-negative as variance cannot be negative.
C) The test statistic must have a chi-squared distribution with n - 1 degrees of freedom to be able to calculate the p-value and assess the significance of the test.

Question 14

Which of the following conditions is needed regarding the chi-squared test statistic for the test of variance?
A)The population random variable must be normal.
B)The test statistic must be a non-negative number.
C)The test statistic must have a chi-squared distribution with n - 1 degrees of freedom.
D)All of these choices are true.

Accepted Answer

All the conditions listed are necessary for the chi-squared test statistic in the context of testing variance. The population must be normally distributed, the test statistic is always non-negative, and it follows a chi-squared distribution with n - 1 degrees of freedom, where n is the sample size.

Question 15

For a 99% confidence interval of the population mean based on a sample of n = 25 with s = 0.05, the critical value of t is:
A)2.7969
B)2.7874
C)2.4922
D)2.4851

Accepted Answer

For a 99% confidence interval with a sample size of n = 25 (which gives us degrees of freedom, df = n - 1 = 24), we use the t-distribution table or calculator to find the critical value. The critical value of t for a 99% confidence interval and df = 24 is approximately 2.7969.

Question 16

Which of the following is not an example illustrating the use of variance?
A)As a measure of risk.
B)As a judge of consistency.
C)To search for and reduce variability in a process.
D)All of these choices are true.

Accepted Answer

All of the choices provided are examples of using variance.

Question 17

When a population is small, we must adjust the test statistic and interval estimator using the ____________________ population correction factor.

Accepted Answer

The answer of When a population is small, we must...

Question 18

The degrees of freedom for the test statistic for m when s is unknown is:
A)1
B)n
C)n - 1
D)None of these choices.

Accepted Answer

When s (the sample standard deviation) is used to estimate the population standard deviation, the degrees of freedom for the test statistic are n - 1, where n is the sample size. This is because one degree of freedom is lost in estimating the population mean from the sample mean.

Question 19

Researchers determine that 60 Puffs tissues is the average number of tissues used during a cold. Suppose a random sample of 100 Puffs users yielded the following data on the number of tissues used during a cold: = 52 and s = 22. Using the sample information provided, the value of the test statistic is: A)t = (52 - 60)\ 22 B)t = (52 - 60)\ (22 \ 100) C)t = (52 - 60)\ (22 \ 100²) D)t = (52 - 60)\ (22 \ 10)

Accepted Answer

The answer of Researchers determine that 60 Puffs tissues is...

Question 20

A random sample of 25 observations is selected from a normally distributed population. The sample variance is 10. In the 95% confidence interval for the population variance, the upper limit is:
A)19.353
B)17.331
C)17.110
D)6.097

Accepted Answer

The answer of A random sample of 25 observations is...

Quiz 11: Inference About a Population

The statistic ( n - 1) s ² \ s ² has a chi-squared distribution with n - 1 degrees of freedom if:

Based on sample data, the 90% confidence interval limits for the population mean are LCL = 170.86 and UCL = 195.42. If the 10% level of significance were used in testing the hypotheses H ₀: m = 201 vs. H ₁: m ¹ 201, the null hypothesis:

A robust estimator is one that is:

The t -test for a population mean is ____________________, meaning that if the population is nonnormal, the results of the test and confidence interval are still valid as long as the nonnormality is not extreme.

When the population standard deviation is unknown and the population is normal, the test statistic for testing hypotheses about m is the - distribution with degrees of freedom.

For statistical inference about the mean of a single population when the population standard deviation is unknown, the degrees for freedom for the t- distribution equal n - 1 because we lose one degree of freedom by using the:

A random sample of size 15 taken from a normally distributed population revealed a sample mean of 75 and a sample variance of 25. The upper limit of a 95% confidence interval for the population mean would equal:

When the population standard deviation is ____________________ and the population is normal, the test statistic for testing hypotheses about m is the t -distribution with n - 1 degrees of freedom.

When the population standard deviation is unknown and the population is ____________________, the test statistic for testing hypotheses about m is the t -distribution with n - 1 degrees of freedom.

Researchers determined that 60 Puffs tissues is the average number of tissues used during a cold. Suppose a random sample of 100 Puffs users yielded the following data on the number of tissues used during a cold: = 52 and s = 22. Suppose the alternative we wanted to test was H ₁: m a = 0.05 is:

Which of the following conditions is needed regarding the chi-squared test statistic for the test of variance?

Which of the following conditions is needed regarding the chi-squared test statistic for the test of variance?

For a 99% confidence interval of the population mean based on a sample of n = 25 with s = 0.05, the critical value of t is:

Which of the following is not an example illustrating the use of variance?

When a population is small, we must adjust the test statistic and interval estimator using the ____________________ population correction factor.

The degrees of freedom for the test statistic for m when s is unknown is:

A random sample of 25 observations is selected from a normally distributed population. The sample variance is 10. In the 95% confidence interval for the population variance, the upper limit is:

Quiz 11: Inference About a Population

The statistic ( n - 1) s 2 \ s 2 has a chi-squared distribution with n - 1 degrees of freedom if:

Based on sample data, the 90% confidence interval limits for the population mean are LCL = 170.86 and UCL = 195.42. If the 10% level of significance were used in testing the hypotheses H 0: m = 201 vs. H 1: m ¹ 201, the null hypothesis:

A robust estimator is one that is:

The t -test for a population mean is ____________________, meaning that if the population is nonnormal, the results of the test and confidence interval are still valid as long as the nonnormality is not extreme.

When the population standard deviation is unknown and the population is normal, the test statistic for testing hypotheses about m is the ____________________- distribution with ____________________ degrees of freedom.

For statistical inference about the mean of a single population when the population standard deviation is unknown, the degrees for freedom for the t- distribution equal n - 1 because we lose one degree of freedom by using the:

A random sample of size 15 taken from a normally distributed population revealed a sample mean of 75 and a sample variance of 25. The upper limit of a 95% confidence interval for the population mean would equal:

When the population standard deviation is ____________________ and the population is normal, the test statistic for testing hypotheses about m is the t -distribution with n - 1 degrees of freedom.

When the population standard deviation is unknown and the population is ____________________, the test statistic for testing hypotheses about m is the t -distribution with n - 1 degrees of freedom.

Researchers determined that 60 Puffs tissues is the average number of tissues used during a cold. Suppose a random sample of 100 Puffs users yielded the following data on the number of tissues used during a cold: = 52 and s = 22. Suppose the alternative we wanted to test was H 1: m a = 0.05 is:

Which of the following conditions is needed regarding the chi-squared test statistic for the test of variance?

Which of the following conditions is needed regarding the chi-squared test statistic for the test of variance?

For a 99% confidence interval of the population mean based on a sample of n = 25 with s = 0.05, the critical value of t is:

Which of the following is not an example illustrating the use of variance?

When a population is small, we must adjust the test statistic and interval estimator using the ____________________ population correction factor.

The degrees of freedom for the test statistic for m when s is unknown is:

A random sample of 25 observations is selected from a normally distributed population. The sample variance is 10. In the 95% confidence interval for the population variance, the upper limit is:

The statistic ( n - 1) s ² \ s ² has a chi-squared distribution with n - 1 degrees of freedom if:

Based on sample data, the 90% confidence interval limits for the population mean are LCL = 170.86 and UCL = 195.42. If the 10% level of significance were used in testing the hypotheses H ₀: m = 201 vs. H ₁: m ¹ 201, the null hypothesis:

When the population standard deviation is unknown and the population is normal, the test statistic for testing hypotheses about m is the - distribution with degrees of freedom.

Researchers determined that 60 Puffs tissues is the average number of tissues used during a cold. Suppose a random sample of 100 Puffs users yielded the following data on the number of tissues used during a cold: = 52 and s = 22. Suppose the alternative we wanted to test was H ₁: m a = 0.05 is: