Question 1

Two hospitals share responsibility for a very poor area of a major city.Both are required to treat patients regardless of their ability to pay.Hospital 1 claims that its emergency room (ER) treats a higher percentage of nonpaying patients than does hospital 2.In a random sample of 200 ER cases from hospital 1, 122 were unable to pay.An independent sample of 180 ER cases from hospital 2 has 108 that were unable to pay.Construct a 99% confidence interval for the population difference in the proportions of nonpaying patients.
A) (-0.1194, -0.1394)
B) (-0.1068, -0.1268)
C) (-0.0884, 0.1084)
D) (-0.1553, 0.1753)

Accepted Answer

The correct answer is A because the 99% confidence interval for the population difference in the proportions of nonpaying patients is (-0.1194, -0.1394). This means that we are 99% confident that the true difference in the proportions of nonpaying patients between the two hospitals is between -0.1194 and -0.1394.

Question 2

To study the effect of soothing music on a person's blood pressure, two random groups of 220 adults were drawn.One group (sample 1) listened to soothing music for 5 min prior to having their blood pressure taken, while the other group (sample 2) sat in silence.From previous studies, it was found that both populations have a standard deviation of 39.18.The average systolic blood pressure from the music group was 114.5.The average systolic blood pressure from the silence group was 122.8.Does the experiment support the conclusion that soothing music significantly lowers average systolic blood pressure better than silence? Select the correct p-value and decision and state the null hypothesis.Use α = 0.01.
A) p-value = 0.0264; fail to reject H₀; The null hypothesis is that there is no significant difference between the two groups.
B) p-value = 0.0264; reject H₀; The null hypothesis is that is a significant difference between the two groups.
C) p-value = 0.0132; fail to reject H₀; The null hypothesis is that there is no significant difference between the two groups.
D) p-value = 0.9736; fail to reject H₀; The null hypothesis is that there is a significant difference between the two groups.

Accepted Answer

C

Question 3

The sampling distribution of the ratio of two sample variances is said to follow an F distribution provided that:
A) the samples are independently drawn from two normal populations.
B) the populations are normal with equal variances.
C) the samples are independent.
D) the samples are independent and the sample sizes are large.

Accepted Answer

The F distribution is used to compare two variances and assumes that the samples are independently drawn from two normal populations.

Question 4

Which of the following options would serve as an intuitive estimate of the parameter  ?
A) 
B) 
C) 
D)

Accepted Answer

The answer of Which of the following options would serve...

Question 5

If the underlying populations are normally distributed and both population variances are equal, the test statistic ​  ​
Follows a:
A) standard normal distribution if both samples are large.
B) Student's t distribution with  degrees of freedom.
C) standard normal distribution with  degrees of freedom.
D) Student's t distribution with  degrees of freedom.

Accepted Answer

The answer of If the underlying populations are normally distributed...

Question 6

Which of the following is NOT a property of the F distribution?
A) F distributions are nonsymmetrical.
B) F can assume only positive values.
C) F distributions have n - 1 degrees of freedom.
D) There are many F distributions and each has a different shape.

Accepted Answer

F distributions have two degrees of freedom, one for the numerator and one for the denominator. Therefore, the correct statement is that F distributions have df1 degrees of freedom in the numerator and df2 degrees of freedom in the denominator, where df1 and df2 are positive integers.

Question 7

In developing a confidence interval estimate for the difference between two population means when the population variances are known, a decrease in the difference  will result in:
A) a wider confidence interval.
B) a narrower confidence interval.
C) a smaller z critical value.
D) the same confidence interval of the same width.

Accepted Answer

The answer of In developing a confidence interval estimate for...

Question 8

A recent survey of pet owners found that 53% of 100 randomly selected cat owners (population 1) and 63% of 100 independently, randomly selected dog owners (population 2) said they would perform cardiopulmonary resuscitation (CPR) on their pets in the event of a medical emergency.Determine a 95% confidence interval for the difference in the population proportion of pet owners who would provide CPR on their pet in the event of an emergency.
A) (-0.2361, 0.0361)
B) (-0.1430, -0.0570)
C) (-0.0142, 0.2142)
D) (-0.2789, 0.0789)

Accepted Answer

The correct answer is A because the 95% confidence interval for the difference in the population proportion of pet owners who would provide CPR on their pet in the event of an emergency is (-0.2361, 0.0361). This interval was calculated using the formula:CI = (p1 - p2) +/- z * sqrt((p1 * (1 - p1) / n1) + (p2 * (1 - p2) / n2))where:p1 = the sample proportion of pet owners who would provide CPR on their cat in the event of an emergencyp2 = the sample proportion of pet owners who would provide CPR on their dog in the event of an emergencyn1 = the sample size of the cat owners surveyn2 = the sample size of the dog owners surveyz = the z-score corresponding to the desired confidence levelIn this case, p1 = 0.53, p2 = 0.63, n1 = 100, n2 = 100, and z = 1.96 (for a 95% confidence level). Plugging these values into the formula, we get:CI = (0.53 - 0.63) +/- 1.96 * sqrt((0.53 * (1 - 0.53) / 100) + (0.63 * (1 - 0.63) / 100))CI = -0.10 +/- 0.1003CI = (-0.2361, 0.0361)

Question 9

College admissions administrators at a university are reevaluating their entrance requirements.They believe that the mean GPA for graduating high school seniors has increased dramatically over the last decade.They randomly sample 85 records of graduating seniors from 10 years ago (sample 1) and find an average GPA of 2.68.An independent random sample of 80 current graduating seniors yields an average GPA of 2.94.If the population variance of high school GPAs is 0.2601, find a 95% confidence interval for the difference in population mean GPA over the last decade.
A) (-0.42, -0.10)
B) (-0.29, -0.13)
C) (-0.36, -0.16)
D) (-0.46, -0.05)

Accepted Answer

The correct answer is A because the 95% confidence interval for the difference in population mean GPA over the last decade is (-0.42, -0.10). This interval is calculated using the formula:CI = (x1 - x2) +/- z * sqrt((s1^2/n1) + (s2^2/n2))where x1 and x2 are the sample means, s1 and s2 are the sample standard deviations, n1 and n2 are the sample sizes, and z is the z-score corresponding to the desired confidence level.In this case, we have:x1 = 2.68x2 = 2.94s1 = sqrt(0.2601) = 0.5101s2 = sqrt(0.2601) = 0.5101n1 = 85n2 = 80z = 1.96 (for a 95% confidence level)Plugging these values into the formula, we get:CI = (2.68 - 2.94) +/- 1.96 * sqrt((0.5101^2/85) + (0.5101^2/80))CI = -0.26 +/- 1.96 * 0.123CI = -0.26 +/- 0.241CI = (-0.42, -0.10)

Question 10

A psychologist is studying the effect of belly stars on Sneetches.A random sample of four Sneetches is drawn, and a test of self-image is given to each Sneetch before and after having the belly star status changed.(If the Sneetch initially had a star, it was removed; if it did not have a star, one was created on the Sneetch using the patented "Star-off/Star-on" procedure.) From the following sample data, construct a 98% confidence interval on the population mean change in self-image associated with a star status change. ​  ​
A) (-26.7977, -4.20232)
B) (-23.4535, -7.5465)
C) (-30.7625, -0.2375)
D) (-37.5519, 6.5519)
​

Accepted Answer

The answer of A psychologist is studying the effect of...

Question 11

In developing a confidence interval estimate for the difference between two population means when the population variances are known, an increase in the size of the samples will result in:
A) a wider confidence interval.
B) a narrower confidence interval.
C) a smaller z critical value.
D) the same confidence interval.

Accepted Answer

Increasing the sample size will result in a decrease in the standard error and a narrower confidence interval. This is because as the sample size increases, the estimate of the population mean becomes more precise and the standard error decreases. Therefore, a larger sample size results in a more accurate estimate of the population mean, hence a narrower confidence interval.

Question 12

If the process of selecting individuals or objects in sample 1 has no effect on, or no relation to, the selection of individuals or objects in sample 2, the samples are:
A) independent.
B) dependent.
C) discrete.
D) paired.

Accepted Answer

If the selection of individuals or objects in sample 1 has no effect on the selection of individuals or objects in sample 2, then the samples are independent. Independent samples are selected randomly and without any relation to each other, and their selection does not affect the probability of selecting other samples. Therefore, option A is the best choice.

Question 13

Two cosmetics manufacturers produce similar hairspray products.Manufacturer 1 asserts that its hairspray holds longer, on average, than does its competitor's product.To test the claim, we randomly sample 20 hairspray users and have half of them use brand 1 hairspray while the other half use brand 2.The average hold time for brand 1 is 18.5 hr with a standard deviation of 6.28 hr.The average hold time for brand 2 is 17.95 hr with a standard deviation of 8.55 hr.Does the sample support manufacturer 1's assertion? Assume that the populations in question are both normal and have unequal variances.Select the appropriate critical value (CV), test statistic (TS), decision and conclusion.(Use α = 0.10).
A) CV = 1.3368; TS = 0.16; reject H₀; Conclusion: There exists a statistically significant difference in hold.
B) CV = 1.3304; TS = -0.23; fail to reject H₀; Conclusion: There is no statistically significant difference in hold.
C) CV = -2.5835; TS = 0.23; reject H₀; Conclusion: There exists a statistically significant difference in hold.
D) CV = 1.3368; TS = 0.16; fail to reject H₀; Conclusion: There is no statistically significant difference in hold.

Accepted Answer

We need to use a two-sample t-test with unequal variances since the population variances are not assumed to be equal. The calculated t-statistic is 0.16 and the appropriate critical value for a two-tailed test with 18 degrees of freedom at α = 0.10 is 1.3368. Since the calculated t-statistic is less than the critical value, we fail to reject the null hypothesis. Therefore, we can conclude that there is no statistically significant difference in hold between the two brands.

Question 14

The pooled estimate for the common variance,  is the weighted average of the two sample variances, where the weights are determined by:
A) the sample standard deviations.
B) the sample variances.
C) the sample sizes.
D) the sample means.

Accepted Answer

The weights for the pooled estimate are determined by the sample sizes. This is because larger sample sizes provide more precise estimates of the population variance, and therefore have a greater influence on the pooled estimate. Thus, option C is the correct choice.

Question 15

In 1993, Toyota introduced the Supra sports car, which was designed to have 320 horsepower in stock configuration.A computer chip modification for the fuel injection system was later introduced that was claimed to increase horsepower.To check whether the chip actually does increase horsepower, we sample six stock 1993 Supras and record each vehicle's horsepower (the results appear below). ​  ​
Next, technicians install the computer chip in each of the six vehicles' electronic injection systems and then record the horsepower of each (the results appear below).
​  ​
Find a 95% confidence interval on the population mean horsepower difference associated with the chip modification.
A) (-6.0150, -0.3183)
B) (-5.3384, -0.9949)
C) (-5.3994, -0.9339)
D) (-5.6055, -0.7279)

Accepted Answer

The answer of In 1993, Toyota introduced the Supra sports...

Question 16

Which of the following options would serve as an intuitive estimate of the parameter  ?
A) 
B) 
C) 
D)

Accepted Answer

The answer of Which of the following options would serve...

Question 17

Concerning inference on two independent population means, which of the following assumptions must be met for the pooled variance estimate to be appropriate?
A) Both  and  .
B) 
C) 
D) Both populations are normally distributed.

Accepted Answer

The answer of Concerning inference on two independent population means,...

Question 18

The test statistic ​  ​
Follows a standard normal distribution if:
A)  and the samples are dependent.
B)  and the samples are dependent.
C) both  and  and the samples are dependent.
D) both  and  and the samples are independent.

Accepted Answer

The test statistic follows a standard normal distribution when both samples are independent and the sample sizes are sufficiently large (n1 ≥ 30 and n2 ≥ 30). The choices A, B, and C mention that the samples are dependent, which means that the assumption of independence is violated. Therefore, the best choice is D, which mentions that both samples are independent.

Question 19

If you wish to estimate the difference between two population means and the population variances are known, a 99% confidence interval estimate can be found by using which of the following critical values?
A) 1.615
B) 1.96
C) 2.33
D) 2.575

Accepted Answer

When estimating the difference between two population means with known variances, and aiming for a 99% confidence interval, the critical value used is from the standard normal (Z) distribution. For a 99% confidence level, the critical value is 2.575, which corresponds to the tails of the distribution (0.5% on each tail in a two-tailed test).

Question 20

Concerning inference on two population proportions, it is appropriate to use the pooled or combined estimate of the common population proportion  when:
A)  .
B)  .
C)  ; that is,  .
D) anytime  .

Accepted Answer

It is appropriate to use the pooled estimate of the common population proportion when the null hypothesis of equal population proportions is accepted. This occurs when the sample proportions are found to be not significantly different from each other, and the pooled estimate is used as the best estimate of the common population proportion. Therefore, choice C is the correct option as it indicates the situation where the null hypothesis is accepted and the pooled estimate is appropriate to use.

Quiz 11: Confidence Intervals and Hypothesis Tests Based on Two Samples or Treatments

The sampling distribution of the ratio of two sample variances is said to follow an F distribution provided that:

Which of the following options would serve as an intuitive estimate of the parameter ?

If the underlying populations are normally distributed and both population variances are equal, the test statistic Follows a:

Which of the following is NOT a property of the F distribution?

In developing a confidence interval estimate for the difference between two population means when the population variances are known, a decrease in the difference will result in:

In developing a confidence interval estimate for the difference between two population means when the population variances are known, an increase in the size of the samples will result in:

If the process of selecting individuals or objects in sample 1 has no effect on, or no relation to, the selection of individuals or objects in sample 2, the samples are:

The pooled estimate for the common variance, is the weighted average of the two sample variances, where the weights are determined by:

Which of the following options would serve as an intuitive estimate of the parameter ?

Concerning inference on two independent population means, which of the following assumptions must be met for the pooled variance estimate to be appropriate?

The test statistic Follows a standard normal distribution if:

If you wish to estimate the difference between two population means and the population variances are known, a 99% confidence interval estimate can be found by using which of the following critical values?

Concerning inference on two population proportions, it is appropriate to use the pooled or combined estimate of the common population proportion when:

Quiz 11: Confidence Intervals and Hypothesis Tests Based on Two Samples or Treatments

The sampling distribution of the ratio of two sample variances is said to follow an F distribution provided that:

Which of the following options would serve as an intuitive estimate of the parameter ?

If the underlying populations are normally distributed and both population variances are equal, the test statistic ​ ​ Follows a:

Which of the following is NOT a property of the F distribution?

In developing a confidence interval estimate for the difference between two population means when the population variances are known, a decrease in the difference will result in:

In developing a confidence interval estimate for the difference between two population means when the population variances are known, an increase in the size of the samples will result in:

If the process of selecting individuals or objects in sample 1 has no effect on, or no relation to, the selection of individuals or objects in sample 2, the samples are:

The pooled estimate for the common variance, is the weighted average of the two sample variances, where the weights are determined by:

Which of the following options would serve as an intuitive estimate of the parameter ?

Concerning inference on two independent population means, which of the following assumptions must be met for the pooled variance estimate to be appropriate?

The test statistic ​ ​ Follows a standard normal distribution if:

If you wish to estimate the difference between two population means and the population variances are known, a 99% confidence interval estimate can be found by using which of the following critical values?

Concerning inference on two population proportions, it is appropriate to use the pooled or combined estimate of the common population proportion when:

If the underlying populations are normally distributed and both population variances are equal, the test statistic Follows a:

The test statistic Follows a standard normal distribution if: