Deck 10: Two-Sample Tests

Question 1

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, give the null and alternative hypotheses to determine if the mean SSATL score of Japanese managers differs from the mean SSATL score of American managers.

A) H₀: μA - μJ ≥ 0 versus H₁: μA - μJ < 0
B) H₀: μA - μJ ≤ 0 versus H₁: μA - μJ > 0
C) H₀: μA - μJ = 0 versus H₁: μA - μJ ≠ 0
D)

Answer 1

H₀: μA - μJ = 0 versus H₁: μA - μJ ≠ 0

Question 2

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

Answer 2

Pooled-variance t test for the difference between two means

Question 3

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

Answer 3

-11.8092

Question 4

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 5

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. The result of the pooled-variance t test of the mean salaries of the females (Population 1) and males (Population 2) 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. Which of the following is an appropriate alternative hypothesis?

A) H₁: μfₑmₐlₑs > μmₐlₑs
B) H₁: μfₑmₐlₑs < μmₐlₑs
C) H₁: μfₑmₐlₑs ≠ μmₐlₑs
D) H₁: μfₑmₐlₑs = μmₐlₑs

Question 6

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

Question 7

If we are testing for the difference between the means of 2 independent populations presuming 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 8

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

Question 9

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

Question 10

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

Question 11

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 12

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 13

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. The result of the pooled-variance t test of the mean salaries of the females (Population 1) and males (Population 2) 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 14

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

Question 15

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 0.10
D) Greater than 0.10

Question 16

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 17

Given the following information, calculate sp², the pooled sample variance that should be used in the pooled-variance t test. s₁² = 4 s₂² = 6
N₁ = 16 n₂ = 25

A) sp² = 6.00
B) sp² = 5.00
C) sp² = 5.23
D) sp² = 4.00

Question 18

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. The result of the pooled-variance t test of the mean salaries of the females (Population 1) and males (Population 2) 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) -6610.
B) -1.3763.
C) -1.7011.
D) 0.0898.

Question 19

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 20

Given the following information, calculate the degrees of freedom that should be used in the pooled-variance t test. s₁² = 4 s₂² = 6
N₁ = 16 n₂ = 25

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

Question 21

TABLE 10-3
A real estate company is interested in testing whether the mean time that families in Gotham have been living in their current homes is less than families in Metropolis. 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.
Gotham: G = 35 months, SG² = 900 Metropolis: M = 50 months, SM² = 1050
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 10-3
A real estate company is interested in testing whether the mean time that families in Gotham have been living in their current homes is less than families in Metropolis. 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.
Gotham: G = 35 months, SG² = 900 Metropolis: M = 50 months, SM² = 1050
Referring to Table 10-3, 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 23

TABLE 10-3
A real estate company is interested in testing whether the mean time that families in Gotham have been living in their current homes is less than families in Metropolis. 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.
Gotham: G = 35 months, SG² = 900 Metropolis: M = 50 months, SM² = 1050
Referring to Table 10-3, 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 24

TABLE 10-3
A real estate company is interested in testing whether the mean time that families in Gotham have been living in their current homes is less than families in Metropolis. 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.
Gotham: G = 35 months, SG² = 900 Metropolis: M = 50 months, SM² = 1050
Referring to Table 10-3, 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 25

TABLE 10-3
A real estate company is interested in testing whether the mean time that families in Gotham have been living in their current homes is less than families in Metropolis. 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.
Gotham: G = 35 months, SG² = 900 Metropolis: M = 50 months, SM² = 1050
Referring to Table 10-3, 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 26

TABLE 10-3
A real estate company is interested in testing whether the mean time that families in Gotham have been living in their current homes is less than families in Metropolis. 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.
Gotham: G = 35 months, SG² = 900 Metropolis: M = 50 months, SM² = 1050
Referring to Table 10-3, which of the following represents the relevant hypotheses tested by the real estate company?

A) H₀: μG - μM ≥ 0 versus H₁: μG - μM < 0
B) H₀: μG - μM ≤ 0 versus H₁: μG - μM > 0
C) H₀: μG - μM = 0 versus H₁: μG - μM ≠ 0
D)

Question 27

TABLE 10-3
A real estate company is interested in testing whether the mean time that families in Gotham have been living in their current homes is less than families in Metropolis. 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.
Gotham: G = 35 months, SG² = 900 Metropolis: M = 50 months, SM² = 1050
Referring to Table 10-3, 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 28

TABLE 10-4
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 10-4, the pooled (i.e., combined) variance is ________.

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. The result of the pooled-variance t test of the mean salaries of the females (Population 1) and males (Population 2) 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 30

TABLE 10-3
A real estate company is interested in testing whether the mean time that families in Gotham have been living in their current homes is less than families in Metropolis. 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.
Gotham: G = 35 months, SG² = 900 Metropolis: M = 50 months, SM² = 1050
Referring to Table 10-3, what is the 95% confidence interval estimate for the difference in the two means?

Question 31

TABLE 10-4
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 10-4, the computed t statistic is ________.

Question 32

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. The result of the pooled-variance t test of the mean salaries of the females (Population 1) and males (Population 2) 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 33

TABLE 10-3
A real estate company is interested in testing whether the mean time that families in Gotham have been living in their current homes is less than families in Metropolis. 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.
Gotham: G = 35 months, SG² = 900 Metropolis: M = 50 months, SM² = 1050
Referring to Table 10-3, 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 34

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. The result of the pooled-variance t test of the mean salaries of the females (Population 1) and males (Population 2) 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 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. The result of the pooled-variance t test of the mean salaries of the females (Population 1) and males (Population 2) 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 36

TABLE 10-3
A real estate company is interested in testing whether the mean time that families in Gotham have been living in their current homes is less than families in Metropolis. 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.
Gotham: G = 35 months, SG² = 900 Metropolis: M = 50 months, SM² = 1050
Referring to Table 10-3, what is the 99% confidence interval estimate for the difference in the two means?

Question 37

TABLE 10-3
A real estate company is interested in testing whether the mean time that families in Gotham have been living in their current homes is less than families in Metropolis. 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.
Gotham: G = 35 months, SG² = 900 Metropolis: M = 50 months, SM² = 1050
Referring to Table 10-3, 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 38

TABLE 10-3
A real estate company is interested in testing whether the mean time that families in Gotham have been living in their current homes is less than families in Metropolis. 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.
Gotham: G = 35 months, SG² = 900 Metropolis: M = 50 months, SM² = 1050
Referring to Table 10-3, 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 39

TABLE 10-3
A real estate company is interested in testing whether the mean time that families in Gotham have been living in their current homes is less than families in Metropolis. 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.
Gotham: G = 35 months, SG² = 900 Metropolis: M = 50 months, SM² = 1050
Referring to Table 10-3, what is the test statistic for the difference between sample means?

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

Question 40

TABLE 10-3
A real estate company is interested in testing whether the mean time that families in Gotham have been living in their current homes is less than families in Metropolis. 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.
Gotham: G = 35 months, SG² = 900 Metropolis: M = 50 months, SM² = 1050
Referring to Table 10-3, 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 41

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

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

Question 42

TABLE 10-4
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 10-4, the p-value for a two-tail test is ________.

Question 43

TABLE 10-4
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 10-4, the critical values for a two-tail test of the null hypothesis of no difference in the population means at the α = 0.05 level of significance are ________.

Question 44

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

Question 45

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.

Question 46

TABLE 10-4
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 10-4, if you were interested in testing against the one-tail alternative that μ₁ > μ₂ at the α = 0.01 level of significance, the null hypothesis would ________ (be rejected/not be rejected).

Question 47

TABLE 10-4
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 10-4, there are ________ degrees of freedom for this test.

Question 48

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 49

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.

Question 50

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

Question 51

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

Question 52

TABLE 10-4
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 10-4, the p-value for a one-tail test (in the hypothesized direction) is ________.

Question 53

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 54

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

Question 55

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

Question 56

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

Question 57

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 58

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

Question 59

TABLE 10-4
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 10-4, what is the 90% confidence interval estimate for the difference in the two means?

Question 60

TABLE 10-4
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 10-4, a two-tail test of the null hypothesis of no difference would ________ (be rejected/not be rejected) at the α = 0.05 level of significance.

Question 61

TABLE 10-6
To investigate the efficacy of a diet, a random sample of 16 male patients is selected from a population of adult males using the diet. The weight of each individual in the sample is taken at the start of the diet and at a medical follow-up 4 weeks later. Assuming that the population of differences in weight before versus after the diet follow a normal distribution, the t test for related samples can be used to determine if there was a significant decrease in the mean weight during this period. Suppose the mean decrease in weights over all 16 subjects in the study is 3.0 pounds with the standard deviation of differences computed as 6.0 pounds.
Referring to Table 10-6, the t test should be ________ -tail.

Question 62

TABLE 10-6
To investigate the efficacy of a diet, a random sample of 16 male patients is selected from a population of adult males using the diet. The weight of each individual in the sample is taken at the start of the diet and at a medical follow-up 4 weeks later. Assuming that the population of differences in weight before versus after the diet follow a normal distribution, the t test for related samples can be used to determine if there was a significant decrease in the mean weight during this period. Suppose the mean decrease in weights over all 16 subjects in the study is 3.0 pounds with the standard deviation of differences computed as 6.0 pounds.
Referring to Table 10-6, there are ________ degrees of freedom for this test.

Question 63

TABLE 10-6
To investigate the efficacy of a diet, a random sample of 16 male patients is selected from a population of adult males using the diet. The weight of each individual in the sample is taken at the start of the diet and at a medical follow-up 4 weeks later. Assuming that the population of differences in weight before versus after the diet follow a normal distribution, the t test for related samples can be used to determine if there was a significant decrease in the mean weight during this period. Suppose the mean decrease in weights over all 16 subjects in the study is 3.0 pounds with the standard deviation of differences computed as 6.0 pounds.
Referring to Table 10-6, the computed t statistic is ________.

Question 64

TABLE 10-6
To investigate the efficacy of a diet, a random sample of 16 male patients is selected from a population of adult males using the diet. The weight of each individual in the sample is taken at the start of the diet and at a medical follow-up 4 weeks later. Assuming that the population of differences in weight before versus after the diet follow a normal distribution, the t test for related samples can be used to determine if there was a significant decrease in the mean weight during this period. Suppose the mean decrease in weights over all 16 subjects in the study is 3.0 pounds with the standard deviation of differences computed as 6.0 pounds.
Referring to Table 10-6, a one-tail test of the null hypothesis of no difference would ________ (be rejected/not be rejected) at the α = 0.05 level of significance.

Question 65

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.
Exam Score Exam Score
Student Before Course (1) After Course (2)
1 530 670
2 690 770
3 910 1,000
4 700 710
5 450 550
6 820 870
7 820 770
8 630 610
Referring to Table 10-5, the calculated value of the test statistic is ________.

Question 66

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.
Exam Score Exam Score
Student Before Course (1) After Course (2)
1 530 670
2 690 770
3 910 1,000
4 700 710
5 450 550
6 820 870
7 820 770
8 630 610
Referring to Table 10-5, in examining the differences between related samples we are essentially sampling from an underlying population of difference "scores."

Question 67

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.
Exam Score Exam Score
Student Before Course (1) After Course (2)
1 530 670
2 690 770
3 910 1,000
4 700 710
5 450 550
6 820 870
7 820 770
8 630 610
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 68

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.
Exam Score Exam Score
Student Before Course (1) After Course (2)
1 530 670
2 690 770
3 910 1,000
4 700 710
5 450 550
6 820 870
7 820 770
8 630 610
Referring to Table 10-5, at the 0.05 level of significance, the conclusion for this hypothesis test is that there is sufficient evidence that

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 69

TABLE 10-6
To investigate the efficacy of a diet, a random sample of 16 male patients is selected from a population of adult males using the diet. The weight of each individual in the sample is taken at the start of the diet and at a medical follow-up 4 weeks later. Assuming that the population of differences in weight before versus after the diet follow a normal distribution, the t test for related samples can be used to determine if there was a significant decrease in the mean weight during this period. Suppose the mean decrease in weights over all 16 subjects in the study is 3.0 pounds with the standard deviation of differences computed as 6.0 pounds.
Referring to Table 10-6, what is the 95% confidence interval estimate for the mean difference in weight before and after the diet?

Question 70

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.
Exam Score Exam Score
Student Before Course (1) After Course (2)
1 530 670
2 690 770
3 910 1,000
4 700 710
5 450 550
6 820 870
7 820 770
8 630 610
Referring to Table 10-5, you must assume that the population of difference scores is normally distributed.

Question 71

TABLE 10-6
To investigate the efficacy of a diet, a random sample of 16 male patients is selected from a population of adult males using the diet. The weight of each individual in the sample is taken at the start of the diet and at a medical follow-up 4 weeks later. Assuming that the population of differences in weight before versus after the diet follow a normal distribution, the t test for related samples can be used to determine if there was a significant decrease in the mean weight during this period. Suppose the mean decrease in weights over all 16 subjects in the study is 3.0 pounds with the standard deviation of differences computed as 6.0 pounds.
Referring to Table 10-6, if we were interested in testing against the two-tail alternative that μD is not equal to zero at the α = 0.05 level of significance, the null hypothesis would ________ (be rejected/not be rejected).

Question 72

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.
Exam Score Exam Score
Student Before Course (1) After Course (2)
1 530 670
2 690 770
3 910 1,000
4 700 710
5 450 550
6 820 870
7 820 770
8 630 610
Referring to Table 10-5, the number of degrees of freedom is

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

Question 73

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 74

TABLE 10-6
To investigate the efficacy of a diet, a random sample of 16 male patients is selected from a population of adult males using the diet. The weight of each individual in the sample is taken at the start of the diet and at a medical follow-up 4 weeks later. Assuming that the population of differences in weight before versus after the diet follow a normal distribution, the t test for related samples can be used to determine if there was a significant decrease in the mean weight during this period. Suppose the mean decrease in weights over all 16 subjects in the study is 3.0 pounds with the standard deviation of differences computed as 6.0 pounds.
Referring to Table 10-6, the p-value for a one-tail test is ________.

Question 75

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.
Exam Score Exam Score
Student Before Course (1) After Course (2)
1 530 670
2 690 770
3 910 1,000
4 700 710
5 450 550
6 820 870
7 820 770
8 630 610
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 76

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.
Exam Score Exam Score
Student Before Course (1) After Course (2)
1 530 670
2 690 770
3 910 1,000
4 700 710
5 450 550
6 820 870
7 820 770
8 630 610
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 77

TABLE 10-6
To investigate the efficacy of a diet, a random sample of 16 male patients is selected from a population of adult males using the diet. The weight of each individual in the sample is taken at the start of the diet and at a medical follow-up 4 weeks later. Assuming that the population of differences in weight before versus after the diet follow a normal distribution, the t test for related samples can be used to determine if there was a significant decrease in the mean weight during this period. Suppose the mean decrease in weights over all 16 subjects in the study is 3.0 pounds with the standard deviation of differences computed as 6.0 pounds.
Referring to Table 10-6, the p-value for a two-tail is ________.

Question 78

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.
Exam Score Exam Score
Student Before Course (1) After Course (2)
1 530 670
2 690 770
3 910 1,000
4 700 710
5 450 550
6 820 870
7 820 770
8 630 610
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 79

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.
Exam Score Exam Score
Student Before Course (1) After Course (2)
1 530 670
2 690 770
3 910 1,000
4 700 710
5 450 550
6 820 870
7 820 770
8 630 610
Referring to Table 10-5, the p-value of the test statistic is ________.

Question 80

TABLE 10-6
To investigate the efficacy of a diet, a random sample of 16 male patients is selected from a population of adult males using the diet. The weight of each individual in the sample is taken at the start of the diet and at a medical follow-up 4 weeks later. Assuming that the population of differences in weight before versus after the diet follow a normal distribution, the t test for related samples can be used to determine if there was a significant decrease in the mean weight during this period. Suppose the mean decrease in weights over all 16 subjects in the study is 3.0 pounds with the standard deviation of differences computed as 6.0 pounds.
Referring to Table 10-6, the critical value for a one-tail test of the null hypothesis of no difference at the α = 0.05 level of significance is ________.