# Quiz 11: Two-Sample Tests of Hypothesis

Statistics

Q 1Q 1

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.

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True False

False

Q 2Q 2

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.

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True False

True

Q 3Q 3

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

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True False

False

Q 4Q 4

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

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True False

Q 5Q 5

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 (n

_{1})(n_{2})− 1.Free

True False

Q 6Q 6

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

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True False

Q 7Q 7

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.

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True False

Q 8Q 8

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

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True False

Q 9Q 9

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.

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True False

Q 10Q 10

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

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True False

Q 11Q 11

A recent study focused on the number of times men and women send a Twitter message in a day. The sample information is summarized here. At the 0.01 significance level,we ask if there is 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

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Multiple Choice

Q 12Q 12

A recent study focused on the number of times men and women send a Twitter message in a day. The information is summarized here. At the 0.01 significance level,we ask if there is 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

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Multiple Choice

Q 13Q 13

A recent study focused on the number of times men and women send a Twitter message in a day. The information is summarized here. At the 0.01 significance level,we ask if there is 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

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Multiple Choice

Q 14Q 14

A recent study focused on the number of times men and women send a Twitter message in a day. The information is summarized here. At the 0.01 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.

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Multiple Choice

Q 15Q 15

A recent study focused on the amount of money single men and women save monthly. The information is summarized here. Assume that the population standard deviations are equal. At the 0.01 significance level,do women save more money than men? What is the test statistic for this hypothesis?
A)t-statistic
B)df-statistic
C)p-statistic
D)z-statistic

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Multiple Choice

Q 16Q 16

A recent study focused on the amount of money single men and women save monthly. The information is summarized here. Assume that the population standard deviations are equal. At the 0.01 significance level,do women save more money than men? What is the critical value for this hypothesis test?
A)+6.213
B)2.33
C)+2.632
D)+2.40

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Multiple Choice

Q 17Q 17

A recent study focused on the amount of money single men and women save monthly. The information is summarized here. Assume that the population standard deviations are equal. At the 0.01 significance level,do women save more money than men? What is the value of the test statistic for this hypothesis test?
A)+2.40
B)+6.213
C)+1.318
D)+2.632

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Multiple Choice

Q 18Q 18

A recent study focused on the amount of money single men and women save monthly. The information is summarized here. Assume that the population standard deviations are equal. At the 0.01 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.

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Multiple Choice

Q 19Q 19

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

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Multiple Choice

Q 20Q 20

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

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Multiple Choice

Q 21Q 21

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

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Multiple Choice

Q 22Q 22

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

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Multiple Choice

Q 23Q 23

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 shown here. 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

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Multiple Choice

Q 24Q 24

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.

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Multiple Choice

Q 25Q 25

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

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Multiple Choice

Q 26Q 26

We test for a hypothesized difference between two population means: H

_{0}: μ_{1}= μ_{2}. 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)27Free

Multiple Choice

Q 27Q 27

For a hypothesis comparing two population means,H

_{0}: μ_{1}≤ 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)+2.064Free

Multiple Choice

Q 28Q 28

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 cannot be true? Assume the population standard deviations are equal.
A)n

_{1}= 11; n_{2}= 13 B)n_{1}= 12; n_{2}= 14 C)n_{1}= 13; n_{2}= 13 D)n_{1}= 10; n_{2}= 16Free

Multiple Choice

Q 29Q 29

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

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Multiple Choice

Q 30Q 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

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Multiple Choice

Q 31Q 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 here. 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)H

_{0}: µ_{A}= µ_{B}B)H_{0}: µ_{A}≠ µ_{B}C)H_{0}: µ_{A}≤ µ_{B}D)H_{0}: µ_{A}> µ_{B}Free

Multiple Choice

Q 32Q 32

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 here. 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)H

_{1}: µ_{A}= µ_{B}B)H_{1}: µ_{A}≠ µ_{B}C)H_{1}: µ_{A}≤ µ_{B}D)H_{1}: µ_{A}> µ_{B}Free

Multiple Choice

Q 33Q 33

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 here. 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

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Multiple Choice

Q 34Q 34

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 here. 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

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Multiple Choice

Q 35Q 35

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 here. 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

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Multiple Choice

Q 36Q 36

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 here. 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.

Free

Multiple Choice

Q 37Q 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 here. 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

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Multiple Choice

Q 38Q 38

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)H

_{0}: µ_{1}= 0 B)H_{0}: µ_{2}= 0 C)H_{0}: µ_{1}= µ_{2}D)H_{0}: µ_{1}≤ µ_{2}Free

Multiple Choice

Q 39Q 39

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)H

_{1}: µ_{1}= 0 B)H_{1}: µ_{2}= 0 C)H_{1}: µ_{1}> µ_{2}D)H_{1}: µ_{1}≤ µ_{2}Free

Multiple Choice

Q 40Q 40

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

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Multiple Choice

Q 41Q 41

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

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Multiple Choice

Q 42Q 42

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. We would like to determine if the LIFO method results in a lower cost of inventory than the FIFO method. What is the null hypothesis?
A)H

_{0}: µ_{d}= 0 B)H_{0}: µ_{d}≠ 0 C)H_{0}: µ_{d}≤ 0 D)H_{0}: µ_{d}≥ 0Free

Multiple Choice

Q 43Q 43

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. We would like to determine if the LIFO method results in a lower cost of inventory than the FIFO method. What is the alternate hypothesis?
A)H

_{1}: µ_{d}= 0 B)H_{1}: µ_{d}≠ 0 C)H_{1}: µ_{d}≤ 0 D)H_{1}: µ_{d}> 0Free

Multiple Choice

Q 44Q 44

An investigation of the effectiveness of a training program to improve customer relationships included a pre-training and a 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 are shown here. 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

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Multiple Choice

Q 45Q 45

An investigation of the effectiveness of a training program to improve customer relationships included a pre-training and a 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 are shown here. For a 0.05 significance level,what is the critical value?
A)1.943
B)1.895
C)1.645
D)2.447

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Multiple Choice

Q 46Q 46

An investigation of the effectiveness of a training program to improve customer relationships included a pre-training and a 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 are shown here. What is the value of the test statistic?
A)1.943
B)1.895
C)2.542
D)2.447

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Multiple Choice

Q 47Q 47

An investigation of the effectiveness of a training program to improve customer relationships included a pre-training and a 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 are shown here. 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.

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Multiple Choice

Q 48Q 48

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 are shown here. What is the null hypothesis?
A)H

_{0}: µ_{d}= 0 B)H_{0}: µ_{d}≠ 0 C)H_{0}: µ_{d}≤ 0 D)H_{0}: µ_{d}≥ 0Free

Multiple Choice

Q 49Q 49

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)H

_{1}: µ_{d}= 0 B)H_{1}: µ_{d}≠ 0 C)H_{1}: µ_{d}> 0 D)H_{1}: µ_{d}< 0Free

Multiple Choice

Q 50Q 50

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 are shown here. What is the value of the test statistic?
A)2.256
B)1.895
C)3.747
D)2.447

Free

Multiple Choice

Q 51Q 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. For a 0.01 significance level,what is the critical value?
A)−2.256
B)−1.895
C)−3.747
D)−2.447

Free

Multiple Choice

Q 52Q 52

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 are shown here. 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.

Free

Multiple Choice

Q 53Q 53

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. We would like to determine if the LIFO method results in a lower cost of inventory than the FIFO method. What are the degrees of freedom?
A)4
B)5
C)15
D)10

Free

Multiple Choice

Q 54Q 54

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. We would like to determine if the LIFO method results 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

Free

Multiple Choice

Q 55Q 55

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. We would like to determine if the LIFO method results 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

Free

Multiple Choice

Q 56Q 56

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.

Free

Multiple Choice

Q 57Q 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? 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

Free

Multiple Choice

Q 58Q 58

When testing the hypothesized equality of two population means,the implied null hypothesis is ________.
A)H

_{0}: µ_{1}= 0 B)H_{0}: µ_{1}− µ_{2 }= 0 C)H_{0}: µ_{2}= 0 D)H_{0}: µ_{1}− µ_{2}≠ 0Free

Multiple Choice

Q 59Q 59

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 n

_{1 }= 37 and n_{2}= 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 = 80Free

Multiple Choice

Q 60Q 60

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 test statistic for the difference between the means?
A)15
B)0.4
C)0.8
D)1.83

Free

Multiple Choice

Q 61Q 61

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

Free

Multiple Choice

Q 62Q 62

The following table shows sample salary information for employees with bachelor's and associate's 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

Free

Multiple Choice