Deck 11: Two-Sample Tests of Hypothesis

Question 1

If the null hypothesis states that there is no difference between the mean net income of retail stores in Chicago and New York City, then the test is two-tailed.

Answer 1

True

Question 2

If the null hypothesis that two means are equal is true, where will 97% of the computed z values lie between?

A) ±2.58
B) ±2.33
C) ±2.17
D) ±2.07

Answer 2

C

Question 3

If the null hypothesis states that there is no difference between the mean income of males and the mean income of females, then the test is one-tailed.

Answer 3

False

Question 4

A recent study focused on the amount of money single men and women save monthly. The information is summarized next. Assume that the population standard deviations are equal. At the .01 significance level, do women save more money than men? What is the critical value for this hypothesis test?

A) +6.213
B) +2.369
C) +2.632
D) +2.40

Question 5

When dependent samples are used to test for differences in the means, we compute paired differences.

Question 6

A recent study focused on the number of times men and women send a Twitter message in a day. The sample information is summarized below. At the .01 significance level, is there a difference in the mean number of times men and women send a Twitter message in a day? What is the test statistic for this hypothesis?

A) z-statistic
B) t-statistic
C) p-statistic
D) df-statistic

Question 7

A recent study focused on the amount of money single men and women save monthly. The information is summarized next. Assume that the population standard deviations are equal. At the .01 significance level, do women save more money than men? What is the test statistic for this hypothesis?

A) z-statistic
B) t-statistic
C) p-statistic
D) df-statistic

Question 8

A recent study focused on the number of times men and women send a Twitter message in a day. The information is summarized next. At the .01 significance level, is there a difference in the mean number of times men and women send a Twitter message in a day? Based on the p-value, what is your conclusion?

A) Reject the null hypothesis and conclude the means are different.
B) Reject the null hypothesis and conclude the means are the same.
C) Fail to reject the null hypothesis.
D) Fail to reject the null hypothesis and conclude the means are different.

Question 9

Assuming the population variances are known, the population variance of the difference between two means is _____________.

A) The sum of the two means
B) The sum of the two population variances
C) The sum of the two population standard deviations
D) The sum of the two sample sizes for each population

Question 10

A recent study focused on the amount of money single men and women save monthly. The information is summarized next. Assume that the population standard deviations are equal. At the .01 significance level, do women save more money than men? What is the value of the test statistic for this hypothesis test?

A) +6.213
B) +1.318
C) +2.632
D) +2.40

Question 11

A recent study focused on the number of times men and women send a Twitter message in a day. The information is summarized next. At the .01 significance level, is there a difference in the mean number of times men and women send a Twitter message in a day? What is the p-value for this hypothesis test?

A) 0.0500
B) 0.0164
C) 0.0001
D) 0.0082

Question 12

If we are testing for the difference between two population means and assume that the two populations have equal and unknown standard deviations, the degrees of freedom are computed as (n₁)(n₂) - 1.

Question 13

If we are testing for the difference between two population means and assume that the two populations have equal but unknown standard deviations, the variances are pooled to compute the best estimated variance.

Question 14

If we are testing for the difference between two population means, it is assumed that the sample observations from one population are independent of the sample observations from the other population.

Question 15

A statistics professor wants to compare grades in two different classes of the same course. This is an example of a paired sample.

Question 16

When dependent samples are used to test for differences in the means, we pool the sample variances.

Question 17

If two dependent samples of size 20 are used to test the difference between the means, the degrees of freedom for a t-statistic are 19.

Question 18

A recent study focused on the amount of money single men and women save monthly. The information is summarized next. Assume that the population standard deviations are equal. At the .01 significance level, what is the conclusion about the way women and men save?

A) Reject the null hypothesis and conclude that women save more than men.
B) Reject the null hypothesis and conclude that women and men save the same amount.
C) Fail to reject the null hypothesis.
D) Fail to reject the null hypothesis and conclude the means are different.

Question 19

When the standard deviations are equal but unknown, a test for the differences between two population means has n - 1 degrees of freedom.

Question 20

A recent study focused on the number of times men and women send a Twitter message in a day. The information is summarized next. At the .01 significance level, is there a difference in the mean number of times men and women send a Twitter message in a day? What is the value of the test statistic for this hypothesis test?

A) 2.668
B) 2.672
C) 2.58
D) 2.40

Question 21

A national manufacturer of ball bearings is experimenting with two different processes for producing precision ball bearings. It is important that the diameters be as close as possible to an industry standard. The output from each process is sampled and the average error from the industry standard is measured in millimeters. The results are presented next. The researcher is interested in determining whether there is evidence that the two processes yield different average errors. The population standard deviations are unknown but are assumed equal. What are the degrees of freedom?

A) 10
B) 13
C) 26
D) 24

Question 22

A national manufacturer of ball bearings is experimenting with two different processes for producing precision ball bearings. It is important that the diameters be as close as possible to an industry standard. The output from each process is sampled and the average error from the industry standard is measured in millimeters. The results are presented next. The researcher is interested in determining whether there is evidence that the two processes yield different average errors. The population standard deviations are unknown but are assumed equal. What is the null hypothesis?

A) H₀: µ_A = µ_B
B) H₀: µ_A ≠ µ_B
C) H₀: µ_A ≤ µ_B
D) H₀: µ_A > µ_B

Question 23

Two samples, one of size 14 and the second of size 13, are selected to test the difference between two population means. How many degrees of freedom are used to find the critical value? Assume the population standard deviations are equal.

A) 27
B) 26
C) 25
D) 14

Question 24

A national manufacturer of ball bearings is experimenting with two different processes for producing precision ball bearings. It is important that the diameters be as close as possible to an industry standard. The output from each process is sampled and the average error from the industry standard is measured in millimeters. The results are presented next. The researcher is interested in determining whether there is evidence that the two processes yield different average errors. The population standard deviations are unknown but assumed equal. What is the critical t value at the 1% level of significance?

A) +2.797
B) -2.492
C) ±1.711
D) ±2.797

Question 25

A national manufacturer of ball bearings is experimenting with two different processes for producing precision ball bearings. It is important that the diameters be as close as possible to an industry standard. The output from each process is sampled and the average error from the industry standard is measured in millimeters. The results are presented next. The researcher is interested in determining whether there is evidence that the two processes yield different average errors. The population standard deviations are unknown but are assumed equal. What is the computed value of t?

A) +2.797
B) -1.000
C) -3.299
D) 0.5938

Question 26

A national manufacturer of ball bearings is experimenting with two different processes for producing precision ball bearings. It is important that the diameters be as close as possible to an industry standard. The output from each process is sampled and the average error from the industry standard is measured in millimeters. The results are presented next. The researcher is interested in determining whether there is evidence that the two processes yield different average errors. The population standard deviations are unknown but are assumed equal. This example is what type of test?

A) A one-sample test of means
B) A two-sample test of means
C) A paired t-test
D) A test of proportions

Question 27

When testing the difference between two dependent population means, the test statistic is based on a ______________.

A) Pooled variance
B) Standard deviation of the differences
C) Pooled proportion
D) Sum of the population variances

Question 28

The results of a mathematics placement exam at two different campuses of Mercy College follow: What is the null hypothesis if we want to test the hypothesis that the mean score on Campus 1 is higher than on Campus 2?

A) H₀: µ₁ = 0
B) H₀: µ₂ = 0
C) H₀: µ₁ = µ₂
D) H₀: µ₁ ≤ µ₂

Question 29

We test for a hypothesized difference between two population means: H₀: μ₁ = μ₂. The population standard deviations are unknown but assumed equal. The number of observations in the first sample is 15, and 12 in the second sample. How many degrees of freedom are associated with the critical value?

A) 24
B) 25
C) 26
D) 27

Question 30

Twenty randomly selected statistics students were given 15 multiple-choice questions and 15 open-ended questions, all on the same material. The professor was interested in determining if students scored higher on the multiple-choice questions. This experiment is an example of ________________.

A) A one-sample test of means
B) A two-sample test of means
C) A paired t-test
D) A test of proportions

Question 31

A national manufacturer of ball bearings is experimenting with two different processes for producing precision ball bearings. It is important that the diameters be as close as possible to an industry standard. The output from each process is sampled and the average error from the industry standard is measured in millimeters. The results are presented next. The researcher is interested in determining whether there is evidence that the two processes yield different average errors. The population standard deviations are unknown but are assumed equal. If we test the null hypothesis at the 1% level of significance, what is the decision?

A) Reject the null hypothesis and conclude the means are different.
B) Reject the null hypothesis and conclude the means are the same.
C) Fail to reject the null hypothesis.
D) Fail to reject the null hypothesis and conclude the means are different.

Question 32

The results of a mathematics placement exam at two different campuses of Mercy College follow: What is the alternative hypothesis if we want to test the hypothesis that the mean score on Campus 1 is higher than on Campus 2?

A) H₁: µ₁ = 0
B) H₁: µ₂ = 0
C) H₁: µ₁ > µ₂
D) H₁: µ₁ ≤ µ₂

Question 33

When testing the difference between two population means, the sample variances are pooled to estimate the population variance when ________________.

A) The population variances are known and equal
B) The population means are known
C) The population variances are assumed unequal and unknown
D) The population variances are assumed equal but unknown

Question 34

When is it appropriate to use the paired difference t-test?

A) When four samples are compared at once
B) When any two samples are compared
C) When two independent samples are compared
D) When two dependent samples are compared

Question 35

For a hypothesis comparing two population means, H₀: μ₁ ≤ μ_2, what is the critical value for a one-tailed hypothesis test, using a 5% significance level, with both sample sizes equal to 13? Assume the population standard deviations are equal.

A) ±1.711
B) +1.711
C) +2.060
D) +2.064

Question 36

The results of a mathematics placement exam at two different campuses of Mercy College follow: What is the computed value of the test statistic?

A) 9.30
B) 2.60
C) 3.37
D) 3.40

Question 37

A national manufacturer of ball bearings is experimenting with two different processes for producing precision ball bearings. It is important that the diameters be as close as possible to an industry standard. The output from each process is sampled and the average error from the industry standard is measured in millimeters. The results are presented next. The researcher is interested in determining whether there is evidence that the two processes yield different average errors. The population standard deviations are unknown but assumed equal. What is the alternate hypothesis?

A) H₁: µ_A = µ_B
B) H₁: µ_A ≠ µ_B
C) H₁: µ_A ≤ µ_B
D) H₁: µ_A > µ_B

Question 38

For a hypothesis test comparing two population means, the combined degrees of freedom are 24. Which of the following statements about the two sample sizes is NOT true? Assume the population standard deviations are equal.

A) n₁ = 11; n₂ = 13
B) n₁ = 12; n₂ = 14
C) n₁ = 13; n₂ = 13
D) n₁ = 10; n₂ = 16

Question 39

Which condition must be met to conduct a test for the difference in two sample means using a z-statistic?

A) The data must be at least of nominal scale.
B) The populations must be normal.
C) The two population standard deviations must be known.
D) The samples are dependent.

Question 40

The net weights (in grams) of a sample of bottles filled by a machine manufactured by Edne, and the net weights of a sample filled by a similar machine manufactured by Orno, Inc., are: Testing the claim at the 0.05 level that the mean weight of the bottles filled by the Orno machine is greater than the mean weight of the bottles filled by the Edne machine, what is the critical value? Assume equal standard deviations for both samples.

A) +2.179
B) +2.145
C) +1.782
D) +1.761

Question 41

Use the following table to determine whether or not there is a significant difference between the average hourly wages at two manufacturing companies. What is the point estimate of the difference between the means?

A) 15
B) 0.4
C) 0.8
D) ­-9

Question 42

An investigation of the effectiveness of a training program to improve customer relationships included a pre-training and post-training customer survey. To compare the differences they computed (post-training survey score - pre-training survey score). Seven customers were randomly selected and completed both surveys. The results follow. For a 0.05 significance level, what is the decision regarding the hypothesis that the training was effective in improving customer relationships?

A) Reject the null hypothesis and conclude that the training was effective.
B) Reject the null hypothesis and conclude that the training was ineffective.
C) Fail to reject the null hypothesis and conclude that the mean survey scores are the same.
D) Fail to reject the null hypothesis and conclude that the mean survey scores are not equal.

Question 43

Consider independent simple random samples that are taken to test the difference between the means of two populations. The variances of the populations are unknown, but are assumed to be equal. The sample sizes of each population are n₁ = 37 and n₂ = 45. The appropriate distribution to use is the:

A) t distribution with df = 82.
B) t distribution with df = 81.
C) t distribution with df = 41.
D) t distribution with df = 80.

Question 44

Accounting procedures allow a business to evaluate their inventory costs based on two methods: LIFO (Last In First Out) or FIFO (First In First Out). A manufacturer evaluated its finished goods inventory (in $000s) for five products with the LIFO and FIFO methods. To analyze the difference, they computed (FIFO - LIFO) for each product. Based on the following results, does the LIFO method result in a lower cost of inventory than the FIFO method? What is the null hypothesis?

A) H₀: µ_d = 0
B) H₀: µ_d ≠ 0
C) H₀: µ_d ≤ 0
D) H₀: µ_d ≥ 0

Question 45

A company is researching the effectiveness of a new website design to decrease the time to access a website. Five website users were randomly selected, and their times (in seconds) to access the website with the old and new designs were recorded. To compare the times, they computed (new website design time - old website design time). The results follow. For a 0.01 significance level, what is the decision regarding the hypothesis that the training was effective in improving customer relationships?

A) Reject the null hypothesis and conclude that the new design reduced the mean access times.
B) Reject the null hypothesis and conclude that the new design did not reduce the mean access times.
C) Fail to reject the null hypothesis.
D) Fail to reject the null hypothesis and conclude that the mean access times are inaccurate.

Question 46

A company is researching the effectiveness of a new website design to decrease the time to access a website. Five website users were randomly selected, and their times (in seconds) to access the website with the old and new designs were recorded. To compare the times, they computed (new website design time - old website design time). The results follow. For a 0.01 significance level, what is the critical value?

A) 2.256
B) 1.895
C) 3.747
D) 2.447

Question 47

A company is researching the effectiveness of a new website design to decrease the time to access a website. Five website users were randomly selected, and their times (in seconds) to access the website with the old and new designs were recorded. To compare the times, they computed (new website design time - old website design time). The results follow. What is the alternative hypothesis?

A) H₁: µ_d = 0
B) H₁: µ_d ≠ 0
C) H₁: µ_d > 0
D) H₁: µ_d < 0

Question 48

Accounting procedures allow a business to evaluate their inventory costs based on two methods: LIFO (Last In First Out) or FIFO (First In First Out). A manufacturer evaluated its finished goods inventory (in $000s) for five products with the LIFO and FIFO methods. To analyze the difference, they computed (FIFO - LIFO) for each product. Based on the following results, does the LIFO method result in a lower cost of inventory than the FIFO method? What is the alternate hypothesis?

A) H₁: µ_d = 0
B) H₁: µ_d ≠ 0
C) H₁: µ_d ≤ 0
D) H₁: µ_d > 0

Question 49

Accounting procedures allow a business to evaluate their inventory costs based on two methods: LIFO (Last In First Out) or FIFO (First In First Out). A manufacturer evaluated its finished goods inventory (in $000s) for five products with the LIFO and FIFO methods. To analyze the difference, they computed (FIFO - LIFO) for each product. Based on the following results, does the LIFO method result in a lower cost of inventory than the FIFO method? What are the degrees of freedom?

A) 4
B) 5
C) 15
D) 10

Question 50

An investigation of the effectiveness of a training program to improve customer relationships included a pre-training and post-training customer survey. To compare the differences they computed (post-training survey score - pre-training survey score). Seven customers were randomly selected and completed both surveys. The results follow. What is the value of the test statistic?

A) 1.943
B) 1.895
C) 2.542
D) 2.447

Question 51

A company is researching the effectiveness of a new website design to decrease the time to access a website. Five website users were randomly selected, and their times (in seconds) to access the website with the old and new designs were recorded. To compare the times, they computed (new website design time - old website design time). The results follow. What is the null hypothesis?

A) H₀: µ_d = 0
B) H₀: µ_d ≠ 0
C) H₀: µ_d ≤ 0
D) H₀: µ_d ≥ 0

Question 52

An investigation of the effectiveness of a training program to improve customer relationships included a pre-training and post-training customer survey. To compare the differences they computed (post-training survey score - pre-training survey score). Seven customers were randomly selected and completed both surveys. The results follow. For a 0.05 significance level, what is the critical value?

A) 1.943
B) 1.895
C) 1.645
D) 2.447

Question 53

Accounting procedures allow a business to evaluate its inventory costs based on two methods: LIFO (Last In First Out) or FIFO (First In First Out). A manufacturer evaluated its finished goods inventory (in $000s) for five products with the LIFO and FIFO methods. To analyze the difference, they computed (FIFO - LIFO) for each product. Based on the following results, does the LIFO method result in a lower cost of inventory than the FIFO method? What is the decision at the 5% level of significance?

A) Fail to reject the null hypothesis and conclude LIFO is more effective.
B) Reject the null hypothesis and conclude LIFO is more effective.
C) Reject the alternate hypothesis and conclude LIFO is more effective.
D) Fail to reject the null hypothesis.

Question 54

A company is researching the effectiveness of a new website design to decrease the time to access a website. Five website users were randomly selected, and their times (in seconds) to access the website with the old and new designs were recorded. To compare the times, they computed (new website design time - old website design time). The results follow. What is the value of the test statistic?

A) 2.256
B) 1.895
C) 3.747
D) 2.447

Question 55

The results of a mathematics placement exam at two different campuses of Mercy College follow: Given that the two population standard deviations are known, what is the p-value?

A) 1.0
B) 0.0
C) 0.05
D) 0.95

Question 56

An investigation of the effectiveness of a training program to improve customer relationships included a pre-training and post-training customer survey. To compare the differences, they computed (post-training survey score - pre-training survey score). Seven customers were randomly selected and completed both surveys. The results follow. This analysis is an example of _____________.

A) A one-sample test of means
B) A two-sample test of means
C) A paired t-test
D) A test of proportions

Question 57

Accounting procedures allow a business to evaluate its inventory costs based on two methods: LIFO (Last In First Out) or FIFO (First In First Out). A manufacturer evaluated its finished goods inventory (in $000s) for five products with the LIFO and FIFO methods. To analyze the difference, they computed (FIFO - LIFO) for each product. Based on the following results, does the LIFO method result in a lower cost of inventory than the FIFO method? What is the value of calculated t?

A) +0.933
B) ±2.776
C) +0.47
D) -2.028

Question 58

Accounting procedures allow a business to evaluate their inventory costs based on two methods: LIFO (Last In First Out) or FIFO (First In First Out). A manufacturer evaluated its finished goods inventory (in $000s) for five products with the LIFO and FIFO methods. To analyze the difference, they computed (FIFO - LIFO) for each product. Based on the following results, does the LIFO method result in a lower cost of inventory than the FIFO method? If you use the 5% level of significance, what is the critical t value?

A) +2.132
B) ±2.132
C) +2.262
D) ±2.228

Question 59

When testing the hypothesized equality of two population means, the implied null hypothesis is ____________.

A) H₀: µ₁ = 0
B) H₀: µ₁ - µ₂ = 0
C) H₀: µ₂ = 0
D) H₀: µ₁ - µ₂ ≠ 0

Question 60

Accounting procedures allow a business to evaluate its inventory costs based on two methods: LIFO (Last In First Out) or FIFO (First In First Out). A manufacturer evaluated its finished goods inventory (in $000s) for five products with the LIFO and FIFO methods. To analyze the difference, they computed (FIFO - LIFO) for each product. Based on the following results, does the LIFO method result in a lower cost of inventory than the FIFO method? This example is what type of test?

A) A one-sample test of means.
B) A two-sample test of means.
C) A paired t-test.
D) A test of proportions.

Question 61

When testing the null hypothesis that two population means are equal, the hypothesized difference between the population means is ________________.

Question 62

If samples taken from two populations are dependent, then a test of ______ differences is applied.

Question 63

When testing for a difference between the means of two dependent samples, n₁ and n₂ are ________________.

Question 64

When independent samples are used to test for differences in the population means with equal but unknown population standard deviations, we _______ these sample standard deviations.

Question 65

When the population standard deviations are unknown, the purpose of pooling the sample variances when testing the difference between two populations is to ___________.

Question 66

A statistics professor wants to compare grades in two different classes of the same course. This is an example of _________ populations.

Question 67

Use the following table to determine whether or not there is a significant difference between the average hourly wages at two manufacturing companies. The p-value is ______.

A) 0.036
B) 0.0336
C) 0.4664
D) 2.58

Question 68

If two dependent samples of size 100 are used to test the difference between the means, the degrees of freedom for a t-statistic are _____.

Question 69

If we are testing for the difference between two population proportions, it is assumed that the sample observations from one population are _____________ of the sample observations from the other population.

Question 70

If the null hypothesis states that there is no difference between the two population means, then the test is ______________.

Question 71

The paired t test is especially appropriate when the two samples are ________.

Question 72

If we are testing for the difference between two population means and assume that the two populations have equal and unknown standard deviations, the standard deviations are ______ to compute a point estimate of the population variance.

Question 73

In one class, a statistics professor wants to compare grades on the first and second exams. This is an example of ________________ observations.

Question 74

The following table shows sample salary information for employees with bachelor's and associate degrees for a large company in the Southeast United States. The point estimate of the difference between the means of the two populations is ______.

A) 32
B) 9
C) -4.5
D) 4.5

Question 75

When dependent samples are used to test for differences in the means, we compute ________________ differences.

Question 76

When independent samples with unknown but equal standard deviations are used to test for differences in the means, we pool the sample _________________.

Question 77

When testing for a difference between the means of two dependent samples, the sample test statistic is a ______________.

Question 78

If a hypothesis states that one population mean is greater than another population mean, then the test is _______________.

Question 79

The paired difference test has ___________ degrees of freedom.

Question 80

When the population standard deviations are equal but unknown, a test for the differences between two populations assumes that the populations are _____________ distributed.