Deck 10: Two-Sample Tests

Question 1

In testing for the differences between the means of two related populations, the ________ hypothesis is the hypothesis of "no differences."

Answer 1

null or H_O

Question 2

Given the following information, calculate s_p², the pooled sample variance that should be used in the pooled-variance t test.

A) s_p² = 6.00
B) s_p² = 5.00
C) s_p² = 5.23
D) s_p² = 4.00

Answer 2

s_p² = 5.23

Question 3

In testing for differences between the means of 2 related populations where the variance of the differences is unknown, the degrees of freedom are

A) n - 1.
B) n₁ + n₂ - 1.
C) n₁ + n₂ - 2.
D) n - 2.

Answer 3

n - 1.

Question 4

In testing for the differences between the means of 2 independent populations where the variances in each population are unknown but assumed equal, the degrees of freedom are

A) n - 1.
B) n₁ + n₂ - 1.
C) n₁ + n₂ - 2.
D) n - 2.

Question 5

TABLE 10-1
Are Japanese managers more motivated than American managers? A randomly selected group of each were administered the Sarnoff Survey of Attitudes Toward Life (SSATL), which measures motivation for upward mobility. The SSATL scores are summarized below.

Referring to Table 10-1, what is the value of the test statistic?

A) -14.08
B) -11.8092
C) -1.9677
D) 96.4471

Question 6

When testing for the difference between 2 population variances with sample sizes of n₁ = 8 and n₂ = 10, where n₁ has the larger variance, the number of degrees of freedom are

A) 8 and 10.
B) 7 and 9.
C) 18.
D) 16.

Question 7

Given the following information, calculate the degrees of freedom that should be used in the pooled-variance t test.

A) df = 41
B) df = 39
C) df = 16
D) df = 25

Question 8

TABLE 10-1
Are Japanese managers more motivated than American managers? A randomly selected group of each were administered the Sarnoff Survey of Attitudes Toward Life (SSATL), which measures motivation for upward mobility. The SSATL scores are summarized below.

Referring to Table 10-1, judging from the way the data were collected, which test would likely be most appropriate to employ?

A) paired t test
B) pooled-variance t test for the difference between two means
C) F test for the ratio of two variances
D) Z test for the difference between two proportions

Question 9

In testing for the differences between the means of two related populations, we assume that the differences follow a ________ distribution.

Question 10

The statistical distribution used for testing the difference between two population variances is the ________ distribution.

A) t
B) standardized normal
C) binomial
D) F

Question 11

The t test for the mean difference between 2 related populations assumes that the

A) population sizes are equal.
B) sample variances are equal.
C) population of differences is approximately normal or sample sizes are large enough.
D) All of the above.

Question 12

In testing for the differences between the means of two independent populations, we assume that the 2 populations each follow a ________ distribution.

Question 13

In testing for differences between the means of two independent populations, the null hypothesis is:

A) H₀ : μ₁ - μ₂ = 2.
B) H₀ : μ₁ - μ₂ = 0.
C) H₀ : μ₁ - μ₂ > 0.
D) H₀ : μ₁ - μ₂ < 2.

Question 14

The test for the equality of two population variances is based on

A) the difference between the 2 sample variances.
B) the ratio of the 2 sample variances.
C) the difference between the 2 population variances.
D) the difference between the sample variances divided by the difference between the sample means.

Question 15

The t test for the difference between the means of 2 independent populations assumes that the respective

A) sample sizes are equal.
B) sample variances are equal.
C) populations are approximately normal.
D) All of the above.

Question 16

The F test used for testing the difference in two population variances is always a one-tail test.

Question 17

If we are testing for the difference between the means of 2 independent populations presumes equal variances with samples of n₁ = 20 and n₂ = 20, the number of degrees of freedom is equal to

A) 39.
B) 38.
C) 19.
D) 18.

Question 18

In what type of test is the variable of interest the difference between the values of the observations rather than the observations themselves?

A) A test for the equality of variances from 2 independent populations.
B) A test for the difference between the means of 2 related populations.
C) A test for the difference between the means of 2 independent populations.
D) All of the above.

Question 19

In testing for differences between the means of two related populations, the null hypothesis is

A) H₀ : μ_D = 2.
B) H₀ : μ_D = 0.
C) H₀ : μ_D < 0.
D) H₀ : μ_D > 0.

Question 20

If we are testing for the difference between the means of 2 related populations with samples of n₁ = 20 and n₂ = 20, the number of degrees of freedom is equal to

A) 39.
B) 38.
C) 19.
D) 18.

Question 21

TABLE 10-3
The use of preservatives by food processors has become a controversial issue. Suppose 2 preservatives are extensively tested and determined safe for use in meats. A processor wants to compare the preservatives for their effects on retarding spoilage. Suppose 15 cuts of fresh meat are treated with preservative I and 15 are treated with preservative II, and the number of hours until spoilage begins is recorded for each of the 30 cuts of meat. The results are summarized in the table below.

Referring to Table 10-3, suppose α = 0.05. Which of the following represents the result of the relevant hypothesis test?

A) The alternative hypothesis is rejected.
B) The null hypothesis is rejected.
C) The null hypothesis is not rejected.
D) Insufficient information exists on which to make a decision.

Question 22

TABLE 10-4
A real estate company is interested in testing whether, on average, families in Gotham have been living in their current homes for less time than families in Metropolis have. Assume that the two population variances are equal. A random sample of 100 families from Gotham and a random sample of 150 families in Metropolis yield the following data on length of residence in current homes.

Referring to Table 10-4, what is a point estimate for the mean of the sampling distribution of the difference between the 2 sample means?

A) -22
B) -10
C) -15
D) 0

Question 23

TABLE 10-1
Are Japanese managers more motivated than American managers? A randomly selected group of each were administered the Sarnoff Survey of Attitudes Toward Life (SSATL), which measures motivation for upward mobility. The SSATL scores are summarized below.

Referring to Table 10-1, find the p-value if we assume that the alternative hypothesis was a two-tail test.

A) smaller than 0.01
B) between 0.01 and 0.05
C) between 0.05 and 0.1
D) greater than 0.1

Question 24

TABLE 10-4
A real estate company is interested in testing whether, on average, families in Gotham have been living in their current homes for less time than families in Metropolis have. Assume that the two population variances are equal. A random sample of 100 families from Gotham and a random sample of 150 families in Metropolis yield the following data on length of residence in current homes.

Referring to Table 10-4, what is(are) the critical value(s) of the relevant hypothesis test if the level of significance is 0.01?

A) t ≅ Z = -1.96
B) t ≅ Z = ±1.96
C) t ≅ Z = -2.080
D) t ≅ Z = -2.33

Question 25

TABLE 10-4
A real estate company is interested in testing whether, on average, families in Gotham have been living in their current homes for less time than families in Metropolis have. Assume that the two population variances are equal. A random sample of 100 families from Gotham and a random sample of 150 families in Metropolis yield the following data on length of residence in current homes.

Referring to Table 10-4, what is the estimated standard error of the difference between the 2 sample means?

A) 4.06
B) 5.61
C) 8.01
D) 16.00

Question 26

TABLE 10-4
A real estate company is interested in testing whether, on average, families in Gotham have been living in their current homes for less time than families in Metropolis have. Assume that the two population variances are equal. A random sample of 100 families from Gotham and a random sample of 150 families in Metropolis yield the following data on length of residence in current homes.

Referring to Table 10-4, which of the following represents the relevant hypotheses tested by the real estate company?

A)
B)
C)
D)

Question 27

TABLE 10-4
A real estate company is interested in testing whether, on average, families in Gotham have been living in their current homes for less time than families in Metropolis have. Assume that the two population variances are equal. A random sample of 100 families from Gotham and a random sample of 150 families in Metropolis yield the following data on length of residence in current homes.

Referring to Table 10-4, what is(are) the critical value(s) of the relevant hypothesis test if the level of significance is 0.05?

A) t ≅ Z = -1.645
B) t ≅ Z = ±1.96
C) t ≅ Z = -1.96
D) t ≅ Z = -2.080

Question 28

TABLE 10-3
The use of preservatives by food processors has become a controversial issue. Suppose 2 preservatives are extensively tested and determined safe for use in meats. A processor wants to compare the preservatives for their effects on retarding spoilage. Suppose 15 cuts of fresh meat are treated with preservative I and 15 are treated with preservative II, and the number of hours until spoilage begins is recorded for each of the 30 cuts of meat. The results are summarized in the table below.

Referring to Table 10-3, what is the value of the test statistic for testing if the population variances differ for preservatives I and II?

Question 29

TABLE 10-2
A researcher randomly sampled 30 graduates of an MBA program and recorded data concerning their starting salaries. Of primary interest to the researcher was the effect of gender on starting salaries. Analysis of the mean salaries of the females and males in the sample is given below.

Referring to Table 10-2, the researcher was attempting to show statistically that the female MBA graduates have a significantly lower mean starting salary than the male MBA graduates. From the analysis in Table 10-2, the correct test statistic is:

A) 0.0860
B) -1.4019
C) -1.7011
D) -6,733.33

Question 30

TABLE 10-2
A researcher randomly sampled 30 graduates of an MBA program and recorded data concerning their starting salaries. Of primary interest to the researcher was the effect of gender on starting salaries. Analysis of the mean salaries of the females and males in the sample is given below.

Referring to Table 10-2, the researcher was attempting to show statistically that the female MBA graduates have a significantly lower mean starting salary than the male MBA graduates. According to the test run, which of the following is an appropriate alternative hypothesis?

A) H₁ : μ_females > μ_males
B) H₁ : μ_females < μ_males
C) H₁ : μ_females ≠ μ_males
D) H₁ : μ_females = μ_males

Question 31

TABLE 10-3
The use of preservatives by food processors has become a controversial issue. Suppose 2 preservatives are extensively tested and determined safe for use in meats. A processor wants to compare the preservatives for their effects on retarding spoilage. Suppose 15 cuts of fresh meat are treated with preservative I and 15 are treated with preservative II, and the number of hours until spoilage begins is recorded for each of the 30 cuts of meat. The results are summarized in the table below.

Referring to Table 10-3,

A) There is no evidence of a difference in the population variances between preservatives I and II.
B) There is evidence of a difference in the population variances between preservatives I and II.
C) There is no evidence that the population variances between preservatives I and II are the same.
D) There is evidence that the population variances between preservatives I and II are the same.

Question 32

TABLE 10-3
The use of preservatives by food processors has become a controversial issue. Suppose 2 preservatives are extensively tested and determined safe for use in meats. A processor wants to compare the preservatives for their effects on retarding spoilage. Suppose 15 cuts of fresh meat are treated with preservative I and 15 are treated with preservative II, and the number of hours until spoilage begins is recorded for each of the 30 cuts of meat. The results are summarized in the table below.

Referring to Table 10-3, state the null and alternative hypotheses for testing if the population variances differ for preservatives I and II.

A)
B)
C)
D)

Question 33

TABLE 10-2
A researcher randomly sampled 30 graduates of an MBA program and recorded data concerning their starting salaries. Of primary interest to the researcher was the effect of gender on starting salaries. Analysis of the mean salaries of the females and males in the sample is given below.

Referring to Table 10-2, what is the 90% confidence interval estimate for the difference between two means?

Question 34

TABLE 10-3
The use of preservatives by food processors has become a controversial issue. Suppose 2 preservatives are extensively tested and determined safe for use in meats. A processor wants to compare the preservatives for their effects on retarding spoilage. Suppose 15 cuts of fresh meat are treated with preservative I and 15 are treated with preservative II, and the number of hours until spoilage begins is recorded for each of the 30 cuts of meat. The results are summarized in the table below.

Referring to Table 10-3, what is the largest level of significance at which a test if the population variances differ for preservatives I and II will not be rejected?

Question 35

TABLE 10-2
A researcher randomly sampled 30 graduates of an MBA program and recorded data concerning their starting salaries. Of primary interest to the researcher was the effect of gender on starting salaries. Analysis of the mean salaries of the females and males in the sample is given below.

Referring to Table 10-2, the researcher was attempting to show statistically that the female MBA graduates have a significantly lower mean starting salary than the male MBA graduates. The proper conclusion for this test is:

A) At the α = 0.10 level, there is sufficient evidence to indicate a difference in the mean starting salaries of male and female MBA graduates.
B) At the α = 0.10 level, there is sufficient evidence to indicate that females have a lower mean starting salary than male MBA graduates.
C) At the α = 0.10 level, there is sufficient evidence to indicate that females have a higher mean starting salary than male MBA graduates.
D) At the α = 0.10 level, there is insufficient evidence to indicate any difference in the mean starting salaries of male and female MBA graduates.

Question 36

TABLE 10-2
A researcher randomly sampled 30 graduates of an MBA program and recorded data concerning their starting salaries. Of primary interest to the researcher was the effect of gender on starting salaries. Analysis of the mean salaries of the females and males in the sample is given below.

Referring to Table 10-2, what is the 99% confidence interval estimate for the difference between two means?

Question 37

TABLE 10-3
The use of preservatives by food processors has become a controversial issue. Suppose 2 preservatives are extensively tested and determined safe for use in meats. A processor wants to compare the preservatives for their effects on retarding spoilage. Suppose 15 cuts of fresh meat are treated with preservative I and 15 are treated with preservative II, and the number of hours until spoilage begins is recorded for each of the 30 cuts of meat. The results are summarized in the table below.

Referring to Table 10-3, what is the critical value for testing if the population variances differ for preservatives I and II at the 5% level of significance?

Question 38

TABLE 10-2
A researcher randomly sampled 30 graduates of an MBA program and recorded data concerning their starting salaries. Of primary interest to the researcher was the effect of gender on starting salaries. Analysis of the mean salaries of the females and males in the sample is given below.

Referring to Table 10-2, what is the 95% confidence interval estimate for the difference between two means?

Question 39

TABLE 10-3
The use of preservatives by food processors has become a controversial issue. Suppose 2 preservatives are extensively tested and determined safe for use in meats. A processor wants to compare the preservatives for their effects on retarding spoilage. Suppose 15 cuts of fresh meat are treated with preservative I and 15 are treated with preservative II, and the number of hours until spoilage begins is recorded for each of the 30 cuts of meat. The results are summarized in the table below.

Referring to Table 10-3, what assumptions are necessary for testing if the population variances differ for preservatives I and II?

A) Both sampled populations are normally distributed.
B) Both samples are random and independent.
C) Neither A nor B is necessary.
D) Both A and B are necessary.

Question 40

TABLE 10-2
A researcher randomly sampled 30 graduates of an MBA program and recorded data concerning their starting salaries. Of primary interest to the researcher was the effect of gender on starting salaries. Analysis of the mean salaries of the females and males in the sample is given below.

Referring to Table 10-2, the researcher was attempting to show statistically that the female MBA graduates have a significantly lower mean starting salary than the male MBA graduates. What assumptions were necessary to conduct this hypothesis test?

A) Both populations of salaries (male and female) must have approximate normal distributions.
B) The population variances are approximately equal.
C) The samples were randomly and independently selected.
D) All of the above assumptions were necessary.

Question 41

TABLE 10-5
To test the effectiveness of a business school preparation course, 8 students took a general business test before and after the course. The results are given below.

Referring to Table 10-5, one must assume that the population of difference scores is normally distributed.

Question 42

The sample size in each independent sample must be the same if we are to test for differences between the means of 2 independent populations.

Question 43

TABLE 10-4
A real estate company is interested in testing whether, on average, families in Gotham have been living in their current homes for less time than families in Metropolis have. Assume that the two population variances are equal. A random sample of 100 families from Gotham and a random sample of 150 families in Metropolis yield the following data on length of residence in current homes.

Referring to Table 10-4, suppose α = 0.10. Which of the following represents the correct conclusion?

A) There is not enough evidence that the mean amount of time families in Gotham have been living in their current homes is less than families in Metropolis.
B) There is enough evidence that the mean amount of time families in Gotham have been living in their current homes is less than families in Metropolis.
C) There is not enough evidence that the mean amount of time families in Gotham have been living in their current homes is not less than families in Metropolis.
D) There is enough evidence that the mean amount of time families in Gotham have been living in their current homes is not less than families in Metropolis.

Question 44

TABLE 10-4
A real estate company is interested in testing whether, on average, families in Gotham have been living in their current homes for less time than families in Metropolis have. Assume that the two population variances are equal. A random sample of 100 families from Gotham and a random sample of 150 families in Metropolis yield the following data on length of residence in current homes.

Referring to Table 10-4, what is the 95% confidence interval estimate for the difference in the two means?

Question 45

TABLE 10-4
A real estate company is interested in testing whether, on average, families in Gotham have been living in their current homes for less time than families in Metropolis have. Assume that the two population variances are equal. A random sample of 100 families from Gotham and a random sample of 150 families in Metropolis yield the following data on length of residence in current homes.

Referring to Table 10-4, what is the standardized value of the estimate of the mean of the sampling distribution of the difference between sample means?

A) -8.75
B) -3.69
C) -2.33
D) -1.96

Question 46

TABLE 10-4
A real estate company is interested in testing whether, on average, families in Gotham have been living in their current homes for less time than families in Metropolis have. Assume that the two population variances are equal. A random sample of 100 families from Gotham and a random sample of 150 families in Metropolis yield the following data on length of residence in current homes.

Referring to Table 10-4, what is the 99% confidence interval estimate for the difference in the two means?

Question 47

TABLE 10-4
A real estate company is interested in testing whether, on average, families in Gotham have been living in their current homes for less time than families in Metropolis have. Assume that the two population variances are equal. A random sample of 100 families from Gotham and a random sample of 150 families in Metropolis yield the following data on length of residence in current homes.

Referring to Table 10-4, suppose α = 0.10. Which of the following represents the result of the relevant hypothesis test?

A) The alternative hypothesis is rejected.
B) The null hypothesis is rejected.
C) The null hypothesis is not rejected.
D) Insufficient information exists on which to make a decision.

Question 48

TABLE 10-4
A real estate company is interested in testing whether, on average, families in Gotham have been living in their current homes for less time than families in Metropolis have. Assume that the two population variances are equal. A random sample of 100 families from Gotham and a random sample of 150 families in Metropolis yield the following data on length of residence in current homes.

Referring to Table 10-4, suppose α = 0.05. Which of the following represents the result of the relevant hypothesis test?

A) The alternative hypothesis is rejected.
B) The null hypothesis is rejected.
C) The null hypothesis is not rejected.
D) Insufficient information exists on which to make a decision.

Question 49

TABLE 10-5
To test the effectiveness of a business school preparation course, 8 students took a general business test before and after the course. The results are given below.

Referring to Table 10-5, at the 0.05 level of significance, the decision for this hypothesis test would be:

A) reject the null hypothesis.
B) do not reject the null hypothesis.
C) reject the alternative hypothesis.
D) It cannot be determined from the information given.

Question 50

TABLE 10-5
To test the effectiveness of a business school preparation course, 8 students took a general business test before and after the course. The results are given below.

Referring to Table 10-5, the p-value of the test statistic is ________.

Question 51

TABLE 10-5
To test the effectiveness of a business school preparation course, 8 students took a general business test before and after the course. The results are given below.

Referring to Table 10-5, what is the critical value for testing at the 5% level of significance whether the business school preparation course is effective in improving exam scores?

A) 2.365
B) 2.145
C) 1.761
D) 1.895

Question 52

TABLE 10-5
To test the effectiveness of a business school preparation course, 8 students took a general business test before and after the course. The results are given below.

Referring to Table 10-5, in examining the differences between related samples we are essentially sampling from an underlying population of difference "scores."

Question 53

TABLE 10-4
A real estate company is interested in testing whether, on average, families in Gotham have been living in their current homes for less time than families in Metropolis have. Assume that the two population variances are equal. A random sample of 100 families from Gotham and a random sample of 150 families in Metropolis yield the following data on length of residence in current homes.

Referring to Table 10-4, suppose α = 0.01. Which of the following represents the result of the relevant hypothesis test?

A) The alternative hypothesis is rejected.
B) The null hypothesis is rejected.
C) The null hypothesis is not rejected.
D) Insufficient information exists on which to make a decision.

Question 54

TABLE 10-4
A real estate company is interested in testing whether, on average, families in Gotham have been living in their current homes for less time than families in Metropolis have. Assume that the two population variances are equal. A random sample of 100 families from Gotham and a random sample of 150 families in Metropolis yield the following data on length of residence in current homes.

Referring to Table 10-4, suppose α = 0.05. Which of the following represents the correct conclusion?

A) There is not enough evidence that the mean amount of time families in Gotham have been living in their current homes is less than families in Metropolis.
B) There is enough evidence that the mean amount of time families in Gotham have been living in their current homes is less than families in Metropolis.
C) There is not enough evidence that the mean amount of time families in Gotham have been living in their current homes is not less than families in Metropolis.
D) There is enough evidence that the mean amount of time families in Gotham have been living in their current homes is not less than families in Metropolis.

Question 55

TABLE 10-4
A real estate company is interested in testing whether, on average, families in Gotham have been living in their current homes for less time than families in Metropolis have. Assume that the two population variances are equal. A random sample of 100 families from Gotham and a random sample of 150 families in Metropolis yield the following data on length of residence in current homes.

Referring to Table 10-4, suppose α = 0.01. Which of the following represents the correct conclusion?

A) There is not enough evidence that the mean amount of time families in Gotham have been living in their current homes is less than families in Metropolis.
B) There is enough evidence that the mean amount of time families in Gotham have been living in their current homes is less than families in Metropolis.
C) There is not enough evidence that the mean amount of time families in Gotham have been living in their current homes is not less than families in Metropolis.
D) There is enough evidence that the mean amount of time families in Gotham have been living in their current homes is not less than families in Metropolis.

Question 56

TABLE 10-5
To test the effectiveness of a business school preparation course, 8 students took a general business test before and after the course. The results are given below.

Referring to Table 10-5, the number of degrees of freedom is

A) 14.
B) 13.
C) 8.
D) 7.

Question 57

TABLE 10-5
To test the effectiveness of a business school preparation course, 8 students took a general business test before and after the course. The results are given below.

Referring to Table 10-5, the value of the standard error of the difference scores is

A) 65.027.
B) 60.828.
C) 22.991.
D) 14.696.

Question 58

TABLE 10-5
To test the effectiveness of a business school preparation course, 8 students took a general business test before and after the course. The results are given below.

Referring to Table 10-5, the value of the sample mean difference is ________ if the difference scores reflect the results of the exam after the course minus the results of the exam before the course.

A) 0
B) 50
C) 68
D) 400

Question 59

TABLE 10-5
To test the effectiveness of a business school preparation course, 8 students took a general business test before and after the course. The results are given below.

Referring to Table 10-5, the calculated value of the test statistic is ________.

Question 60

TABLE 10-5
To test the effectiveness of a business school preparation course, 8 students took a general business test before and after the course. The results are given below.

Referring to Table 10-5, at the 0.05 level of significance, the conclusion for this hypothesis test would be:

A) the business school preparation course does improve exam score.
B) the business school preparation course does not improve exam score.
C) the business school preparation course has no impact on exam score.
D) No conclusion can be drawn from the information given.

Question 61

When testing for differences between the means of 2 related populations, we can use either a one-tail or two-tail test.

Question 62

For all two-sample tests, the sample sizes must be equal in the 2 groups.

Question 63

When we test for differences between the means of 2 independent populations, we can only use a two-tail test.

Question 64

When testing H₀ : π₁ - π₂ ≤ 0 versus H₁ : π₁ - π₂ > 0, the observed value of the Z-score was found to be -2.13. The p-value for this test would be

A) 0.0166.
B) 0.0332.
C) 0.9668.
D) 0.9834.

Question 65

When testing H₀ : π₁ - π₂ = 0 versus H₁ : π₁ - π₂ ≠ 0, the observed value of the Z-score was found to be -2.13. The p-value for this test would be

A) 0.0166.
B) 0.0332.
C) 0.9668.
D) 0.9834.

Question 66

TABLE 10-6
Two samples each of size 25 are taken from independent populations assumed to be normally distributed with equal variances. The first sample has a mean of 35.5 and standard deviation of 3.0 while the second sample has a mean of 33.0 and standard deviation of 4.0.
Referring to Table 10-6, the computed t statistic is ________.

Question 67

F tests are one-tail tests.

Question 68

When testing H₀ : π₁ - π₂ ≥ 0 versus H₁ : π₁ - π₂ < 0, the observed value of the Z-score was found to be -2.13. The p-value for this test would be

A) 0.0166.
B) 0.0332.
C) 0.9668.
D) 0.9834.

Question 69

TABLE 10-6
Two samples each of size 25 are taken from independent populations assumed to be normally distributed with equal variances. The first sample has a mean of 35.5 and standard deviation of 3.0 while the second sample has a mean of 33.0 and standard deviation of 4.0.
Referring to Table 10-6, the pooled (i.e., combined) variance is ________.

Question 70

Repeated measurements from the same individuals is an example of data collected from 2 related populations.

Question 71

When the sample sizes are equal, the pooled variance of the 2 groups is the average of the 2 sample variances.

Question 72

A statistics professor wanted to test whether the grades on a statistics test were the same for upper and lower classmen. The professor took a random sample of size 10 from each, conducted a test and found out that the variances were equal. For this situation, the professor should use a t test with related samples.

Question 73

A researcher is curious about the effect of sleep on students' test performances. He chooses 60 students and gives each 2 tests: one given after 2 hours' sleep and one after 8 hours' sleep. The test the researcher should use would be a related samples test.

Question 74

The test for the equality of 2 population variances assumes that each of the 2 populations is normally distributed.

Question 75

The F distribution can only have positive values.

Question 76

A statistics professor wanted to test whether the grades on a statistics test were the same for upper and lower classmen. The professor took a random sample of size 10 from each, conducted a test and found out that the variances were equal. For this situation, the professor should use a t test with independent samples.

Question 77

A Marine drill instructor recorded the time in which each of 11 recruits completed an obstacle course both before and after basic training. To test whether any improvement occurred, the instructor would use a t-distribution with 10 degrees of freedom.

Question 78

TABLE 10-6
Two samples each of size 25 are taken from independent populations assumed to be normally distributed with equal variances. The first sample has a mean of 35.5 and standard deviation of 3.0 while the second sample has a mean of 33.0 and standard deviation of 4.0.
Referring to Table 10-6, there are ________ degrees of freedom for this test.

Question 79

The F distribution is symmetric.

Question 80

A Marine drill instructor recorded the time in which each of 11 recruits completed an obstacle course both before and after basic training. To test whether any improvement occurred, the instructor would use a t-distribution with 11 degrees of freedom.