Deck 9: Testing the Difference Between Two Means, Two Variances, and Two Proportions

Question 1

If the test value for the difference between the means of two large samples is 2.57 when the critical value is 1.96, what decision should be made?

A) Reject the null hypothesis.
B) Accept the null hypothesis.
C) Reject the alternative hypothesis.
D) Accept the equality hypothesis.

Answer 1

A

Question 2

An educational researcher is analyzing the test scores for physics students taught using two different methods - a traditional method, and a web-based self-paced method. Can he conclude, at = .05, that the test scores in the web-based self-paced method are lower?

A) The data supports the claim because the test value 1.68 is greater than than the critical value 1.65.
B) The data supports the claim because the test value 1.68 is less than than the critical value 1.96.
C) The data supports the claim because the test value 3.66 is greater than than the critical value 1.96.
D) The data supports the claim because the test value 3.66 is greater than than the critical value 1.65.

Answer 2

D

Question 3

A sociologist expects the life expectancy of people in Africa is different than the life expectancy of people in Asia. The data obtained is shown in the table below. Determine the 95% confidence interval for the difference in the population means.

A)
B)
C)
D)

Answer 3

B

Question 4

A pharmaceutical company is testing the effectiveness of a new drug for lowering cholesterol. As part of this trial, they wish to determine whether there is a difference between the effectiveness for women and men.
At = 0.05, what is an appropriate test value?

A) -2.60
B) 0.34
C) -1.13
D) -0.88

Question 5

The average credit card debt for a recent year was $9540. Five years earlier the average credit card debt was $8880. Assume sample sizes of 34 were used and the population standard deviations of both samples were $1069. Is there evidence to conclude that the average credit card debt has increased? Use .
a. State the hypotheses.
b. Find the critical value.
c. Compute the test statistic.
d. Make the decision.
e. Summarize the results.

Question 6

The formula used in the z test for comparing the means from two independent populations is _______________.

Question 7

A bond analyst is analyzing the interest rates for equivalent municipal bonds issued by two different states. At α = 0.05, is there enough evidence to conclude that there is a difference in the interest rates paid by the two states?

A) Yes, because the test value -11.16 is outside the critical region
B) Yes, because the test value -3.11 is outside the critical region
C) Yes, because the test value 124.44 is outside the critical region
D) No, because the test value -0.01 is inside the critical region

Question 8

The standard deviation of the difference in means of two large samples is .

Question 9

When comparing the means of samples from two normally distributed populations, if the samples are independent and the population variances are known, the z test can be used.

Question 10

A group of college students believes the average grades in psychology courses are different than the average grades in biology courses. The group found the average psychology grades of a sample of 8 students was 86.4 and the average biology grades of a sample of 10 students was 82.2. What is the null hypothesis for this study?

A)
B)
C)
D)

Question 11

Consider the null hypothesis . If the confidence interval for does not contain 0, the null hypothesis should be rejected.

Question 12

Joan has just moved into a new apartment and wants to purchase a new couch. To determine if there is a difference between the average prices of couches at two different stores, she collects the following data. Test the hypothesis that there is no difference in the average price. Use α = 0.05.

Question 13

An field researcher is gathering data on the trunk diameters of mature pine and spruce trees in a certain area. The following are the results of his random sampling. Can he conclude, at = 0.10, that the average trunk diameter of a pine tree is greater than the average diameter of a spruce tree?

A) The data does not support the conclusion that the average pine tree trunks are larger because the test value 0.53 is less than than the critical value1.28.
B) The data does not support the conclusion that the average pine tree trunks are larger because the test value 1.03 is less than than the critical value 1.28.
C) The data does not support the conclusion that the average pine tree trunks are larger because the test value 1.03 is less than than the critical value 1.65.
D) The data does not support the conclusion that the average pine tree trunks are larger because the test value 23.05 is greater than than the critical value 1.65.

Question 14

In October, the campus bookstore asked a random set of freshmen and seniors how much they had spent on textbooks that semester. The bookstore believes that the two groups spent the same amount. What is an appropriate test value for a z test?

A) 0.29
B) 8.35
C) 2.40
D) 1.23

Question 15

Use the following to answer questions
A sociologist wants to determine if the life expectancy of people in Africa is less than the life expectancy of people in Asia. The data obtained is shown in the table below.
What is an appropriate null hypothesis?

A)
B)
C)
D)

Question 16

A conservationist suspects that the water level in Horseshoe Lake has been affected more by the current drought than the water level in Swan Lake, so he measures how far the water level is below normal each day in June. The data are normally distributed. Test his hypothesis at α = 0.01.

Question 17

Use the following to answer questions
A sociologist wants to determine if the life expectancy of people in Africa is less than the life expectancy of people in Asia. The data obtained is shown in the table below.
Calculate the critical value. Use α = 0.05.

A) -1.65
B) -2.33
C) -2.58
D) -1.96

Question 18

If the test value for the difference between the means of two large samples is 1.43 when the critical value is 1.96, the null hypothesis should not be rejected.

Question 19

Use the following to answer questions
A sociologist wants to determine if the life expectancy of people in Africa is less than the life expectancy of people in Asia. The data obtained is shown in the table below.
What is the test value?

A) -5.38
B) -3.70
C) -1.86
D) -0.47

Question 20

A marketing firm asked a random set of married and single men how much they were willing to spend on a vacation. Is there sufficient evidence at α = 0.05 to conclude that is there a difference in the two amounts?

A) No, because the test value 0.23 is inside the critical region .
B) Yes, because the test value 4.16 is outside the critical region .
C) Yes, because the test value 1.60 is inside the critical region .
D) No, because the test value 1.60 is outside the critical region .

Question 21

Use the following to answer questions
A researcher wanted to determine if using an octane booster would increase gasoline mileage. A random sample of seven cars was selected; the cars were driven for two weeks without the booster and two weeks with the booster. Use the definitions of X₁ and X₂ as given in the table. Consequently, D = X₁-X₂.
What critical value should be used at α = 0.05?

A) -2.447
B) -2.365
C) -1.943
D) -1.895

Question 22

Use the following to answer questions
Mauricio Cruz, a wine merchant for Cruz's Spirits Emporium, wants to determine if the average price of imported wine is less than the average price of domestic wine. He obtained the data shown in the table below.
What is the critical value at α = 0.05?

A) -1.761
B) -1.753
C) -2.145
D) -2.131

Question 23

Use the following to answer questions
Mauricio Cruz, a wine merchant for Cruz's Spirits Emporium, wants to determine if the average price of imported wine is less than the average price of domestic wine. He obtained the data shown in the table below.
What is the appropriate test value for a t test?

A) -6.49
B) -4.46
C) -2.54
D) -0.92

Question 24

A medical researcher is interested in whether patients' left arms or right arms are longer. If 10 patients participate in this study, how many degrees of freedom should the researcher use when finding the critical value for a t test?

A) 9
B) 10
C) 18
D) 19

Question 25

The number of calories in a 12-ounce serving of randomly-selected regular and lite beers is listed. Is there sufficient evidence to conclude that the mean number of calories for lite beers is significantly less than that for the regular beers? Use . Assume the variables are approximately normally distributed. a.State the hypotheses.
b. Find the critical value(s).
c. Compute the test value.
d. Make the decision.
e. Summarize the results.

Question 26

Samples are independent when they are not related.

Question 27

Use the following to answer questions
A researcher wanted to determine if using an octane booster would increase gasoline mileage. A random sample of seven cars was selected; the cars were driven for two weeks without the booster and two weeks with the booster. Use the definitions of X₁ and X₂ as given in the table. Consequently, D = X₁-X₂.
State the alternative hypothesis?

A)
B)
C)
D)

Question 28

Use the following to answer questions
A researcher wanted to determine if using an octane booster would increase gasoline mileage. A random sample of seven cars was selected; the cars were driven for two weeks without the booster and two weeks with the booster. Use the definitions of X₁ and X₂ as given in the table. Consequently, D = X₁-X₂.
Determine the mean of the differences.

A) -1.67
B) 6.3
C) 1.67
D) -1.43

Question 29

Twelve dieters lost an average of 9.8 pounds in 6 weeks when given a special diet plus a "fat-blocking" herbal formula. A control group of twelve other dieters were given the same diet, but without the herbal formula, and lost an average of 8.8 pounds during the same time. The standard deviation of the "fat-blocker" sample was 2.6 and the standard deviation of the control group was 2.8. Find the 95% confidence interval for the differences of the means.

A)
B)
C)
D)

Question 30

In a test of the difference between the two means below, what should the test value be for a t test?

A) -0.31
B) -0.18
C) -0.89
D) -6.98

Question 31

A running coach wanted to see whether runners ran faster after eating spaghetti the night before. A group of six runners was randomly chosen for this study. Each ran a 5 kilometer race after having a normal dinner the night before, and then a week later, reran the same race after having a spaghetti dinner the night before. The times for their races are shown in the table below. What test value should be used in a t test for these dependent samples?

A) 5.07
B) 1.07
C) 2.07
D) 2.62

Question 32

When the subjects are paired or matched in some way, samples are considered to be _______________.

Question 33

Use the following to answer questions
A researcher wanted to determine if using an octane booster would increase gasoline mileage. A random sample of seven cars was selected; the cars were driven for two weeks without the booster and two weeks with the booster. Use the definitions of X₁ and X₂ as given in the table. Consequently, D = X₁-X₂.
Compute the standard deviation of the differences.

A) 0.84
B) 0.78
C) 0.13
D) 0.11

Question 34

A local charity believes they receive more money from people in the River Heights neighborhood than from people in the Lakeview neighborhood. They conducted a survey of 24 people randomly selected form each neighborhood and recorded the results. At α = 0.01, is their hypothesis correct?

Question 35

A marketing firm asked a random set of married women and married men how much they were willing to spend for jewelry as a present for their spouse. Can the firm conclude, at = 0.05, that the two groups have a different willingness to spend?

A) No, because the test value -0.65 is inside the noncritical region
B) Yes, because the test value -5.99 is outside the noncritical region
C) Yes, because the test value -0.75 is inside the noncritical region
D) No, because the test value -0.75 is outside the noncritical region

Question 36

Which of the following represent dependent samples.
I) Life spans of pairs of siblings.
Ii) Life spans of randomly-selected pairs of people
Iii) Life spans of pairs of mothers and daughters

A) i
B) i and iii
C) iii
D) i, ii, and iii

Question 37

When subjects are matched according to one variable, the matching process does not eliminate the influence of other variables.

Question 38

The Donaldson Corporation wants to hire a temporary secretary. There are two employment agencies in town, and it is believed that the average hourly wage charged by both agencies is the same. A Donaldson manager surveyed other employers in town to find what they paid the agencies for temporary secretaries. The results are summarized below. At , test the claim that each agency charges the same hourly wage.

Question 39

A reporter bought hamburgers at randomly selected stores of two different restaurant chains, and had the number of Calories in each hamburger measured. Can the reporter conclude, at = 0.05, that the hamburgers from the two chains have a different number of Calories?

A) No, because the test value -0.23 is inside the noncritical region
B) Yes, because the test value -0.23 is inside the noncritical region
C) Yes, because the test value -2.82 is outside the noncritical region
D) No, because the test value -1.29 is inside the noncritical region

Question 40

Use the following to answer questions
Mauricio Cruz, a wine merchant for Cruz's Spirits Emporium, wants to determine if the average price of imported wine is less than the average price of domestic wine. He obtained the data shown in the table below.
What is the null hypothesis?

A)
B)
C)
D)

Question 41

Two groups were polled about their attitudes towards capital punishment. In one group 30 out of 100 favored capital punishment, and in the other group 40 out of 80 favored capital punishment. Calculate an appropriate test value test the hypothesis that the population proportions are the same.

A) -2.73
B) -37.40
C) -0.20
D) -13.68

Question 42

Many elementary school students in a school district currently have ear infections. A random sample of children in two different schools found that 17 of 50 at one school and 15 of 30 at the other have ear infections. At the 0.05 level of significance, is there sufficient evidence to support the claim that a difference exists between the proportions of students who have ear infections at the two schools?

A) Yes, because the test value -12.50 is outside the noncritical region -1.96 < z < 1.96.
B) No, because the test value -1.41 is inside the noncritical region -1.96 < z < 1.96.
C) No, because the test value -1.85 is inside the noncritical region -1.96 < z < 1.96.
D) Yes, because the test value -6.96 is outside the noncritical region -1.96 < z < 1.96.

Question 43

Find the proportion given n = 32 and X = 8.

A) 0.75
B) 0.2
C) 0.8
D) 0.25

Question 44

For the samples summarized below, test the hypothesis, at α = 0.05, that the two variances are different.

A) Reject the hypothesis because the test value 3.06 is less than the critical value 3.34.
B) Reject the hypothesis because the test value 3.06 is less than the critical value 2.61.
C) Accept the hypothesis because the test value 9.38 is greater than the critical value 3.16.
D) Reject the hypothesis because the test value 9.38 is greater than the critical value 2.74.

Question 45

Find and , if , , , and .

Question 46

One uses a t test when comparing two variances or standard deviations.

Question 47

The critical value for a left-tailed t test for dependent samples is ___________ when there are seven degrees of freedom and α = 0.025.

Question 48

When finding the test value for an F test, the smaller of the two variances should be placed in the numerator.

Question 49

In the F distribution the mean value of F is approximately equal to __________.

Question 50

The formula of the test value to be used in a t test for dependent samples is ______________.

Question 51

In the F distribution, values of F cannot be negative, because variances are always positive or zero.

Question 52

To determine whether two sample variances are equal, a researcher can use a(n) __________.

Question 53

A recent survey reported that in a sample of 300 students who attend two-year colleges, 105 work at least 20 hours per week. Additionally, in a sample of 225 students attending private four-year universities, only 20 students work at least 20 hours per week. What is the test value for a test of the difference between these two population proportions?

A) 6.95
B) 7.61
C) 2.38
D) 4.18

Question 54

Find and , if , , , and .

A)
B)
C)
D)

Question 55

Find X, given and n = 28.

A) 17
B) 8
C) 4
D) 11

Question 56

68% of students at a university live on campus. A random sample found that 24 of 40 male students and 43 of 55 of female students live on campus. At the 0.05 level of significance, is there sufficient evidence to support the claim that a difference exists between the proportions of male and female students who live on campus?

A) Yes, because the test value -20.26 is outside the noncritical region -1.96 < z < 1.96.
B) No, because the test value -0.96 is inside the noncritical region -1.96 < z < 1.96.
C) Yes, because the test value -4.21 is outside the noncritical region -1.96 < z < 1.96.
D) No, because the test value -1.92 is inside the noncritical region -1.96 < z < 1.96.

Question 57

A study of cats and dogs found that 39 of 60 cats and 21 of 50 dogs slept more than 10 hours per day. At the 0.05 level of significance, is there sufficient evidence to conclude that a difference exists between the proportions of cats and dogs that sleep more than 10 hours per day?

A) Yes, because the test value 2.41 is outside the noncritical region -1.96 < z < 1.96.
B) Yes, because the test value 2.80 is outside the noncritical region -1.65 < z < 1.65.
C) Yes, because the test value 6.32 is outside the noncritical region -1.65 < z < 1.65.
D) Yes, because the test value 7.81 is outside the noncritical region -1.96 < z < 1.96.

Question 58

A poll found that 37% of male voters and 42% of female voters support a particular candidate. To test whether this candidate has equal levels of support between male and female voters, the alternative hypothesis should be

A) .
B) .
C) .
D) .

Question 59

A poll found that 47% of male voters and 50% of female voters support a particular candidate. To test whether this candidate has equal levels of support between male and female voters, the null hypothesis should be

A) .
B) .
C) .
D) .

Question 60

Determine the value of α as shown below in the graph of an F distribution. The degrees of freedom for the numerator are seven, and the degrees of freedom for the denominator are nine.

A) 0.01
B) 0.025
C) 0.05
D) 0.1

Question 61

A researcher hypothesized that the variation in the car rental rates (in US$/day) at a major city airport is less than in the car rental rates down town. A survey found that the variance of the rental rates on 7 cars at the airport was 25.7 while the variance of the rental rates on 6 cars down town was 60.4. What test value should be used in a F test?

A) 2.74
B) 1.53
C) 2.35
D) 5.52

Question 62

The critical value for a two-tailed F test is 2.65 when α = 0.05, the sample size from which the variance for the numerator was obtained is 10, and the sample size from which the variance for the denominator was obtained is 15.

Question 63

In comparing the two standard deviations below, what test value and degrees of freedom should be used in an F test?

A) test value = 2.33; d.f.N. = 19 and d.f.D. = 24
B) test value = 2.33; d.f.N. = 23 and d.f.D. = 18
C) test value = 5.44; d.f.N. = 24 and d.f.D. = 19
D) test value = 5.44; d.f.N. = 18 and d.f.D. = 23

Question 64

A researcher hypothesizes that the variation in the amount of money spent on business dinners is greater than the amount spent on lunches. The variance of the cost of nine business dinners (in US$) was 6.12 and the variance on 12 lunches was 0.87. What test value should be used in an F test?

A) 2.65
B) 9.61
C) 49.5
D) 7.03

Question 65

The critical value for a right-tailed F test is 2.57 when α = 0.025, the degrees of freedom for the numerator are 15, and the degrees of freedom for the denominator are 20.

Question 66

A car salesman claims that the variance of prices on convertibles is higher than the variance of prices on station wagons. The standard deviation of the list price on 16 convertibles is $6800 and the standard deviation on 24 station wagons is $3900. What should the test value be?

A) 1.74
B) 3.04
C) 2.25
D) 1.53

Question 67

Use Table H from the textbook to find the critical value for a right-tailed F test with α = 0.05, d.f.N. = 21, and d.f.D. = 20.

A) 2.12
B) 2.23
C) 2.20
D) 2.16

Question 68

What is the critical value for a two-tailed F test with α = 0.10, when the sample size from which the variance for the numerator was obtained is 10, and the sample size from which the denominator was obtained is 24?

A) 2.27
B) 2.25
C) 2.32
D) 2.30

Question 69

For the samples summarized below, test the hypothesis that the two variances are equal, at α = 0.05

A) Accept the hypothesis because the test value 8.27 is greater than the critical value 2.88.
B) Reject the hypothesis because the test value 2.87 is less than the critical value 2.77.
C) Reject the hypothesis because the test value 8.27 is greater than the critical value 2.77.
D) Accept the hypothesis because the test value 2.87 is less than the critical value 2.88.

Question 70

Given the variances of the two samples below, find the test value and the degrees of freedom that should be used in an F test.

A) test value = 2.94; d.f.N. = 26 and d.f.D. = 14
B) test value = 0.58; d.f.N. = 25 and d.f.D. = 13
C) test value = 1.71; d.f.N. = 25 and d.f.D. = 13
D) test value = 1.31; d.f.N. = 26 and d.f.D. = 14