Deck 10: Two-Sample Hypothesis Tests

Question 1

The critical value in an F test for equal variances is the ratio of the sample variances.

Answer 1

False

Question 2

The F distribution is never negative and is always skewed right.

Answer 2

True

Question 3

In comparing the means of two independent samples,if the test statistic indicates a significant difference at α =.05,it will also be significant at α = .10.

Answer 3

True

Question 4

In general,the Welch-Satterthwaite t-test for two means has the same degrees of freedom as the pooled samples t-test for two means.

Question 5

We could use the same data set for two independent samples (i.e. ,two columns of data)either to compare the means (t-test)or to compare the variances (F test).

Question 6

When testing the difference between two population proportions,it is necessary to use the same size sample from each population.

Question 7

When sample data occur in pairs,an advantage of choosing a paired t-test is that it tends to increase the power of a test,as compared to treating each sample independently.

Question 8

The difference between two sample proportions p1 − p2 may be assumed normally distributed if each sample has at least 10 "successes" and 10 "failures."

Question 9

The degrees of freedom for the t-test used to compare two population means (independent samples)with unknown variances (assumed equal)will be n1 + n2 − 2.

Question 10

The t-test for two samples of paired data will use n differences,making it a one-sample t-test.

Question 11

In conducting a paired t-test of the difference between two population means,the usual null hypothesis is that the mean of the population of paired differences is zero.

Question 12

When using independent samples to test the difference between two population means,a pooled variance is used if the population variances are unknown and assumed equal.

Question 13

A paired t-test with two columns of 10 observations in each column would use d.f.= 18.

Question 14

The test statistic in an F test for equal variances is the ratio of the sample variances.

Question 15

In an F test for the ratio of two population variances,the degrees of freedom in both the numerator and the denominator must be equal.

Question 16

The Welch-Satterthwaite test is more conservative than the pooled variance test to compare two population means with unknown variances in independent samples.

Question 17

A pooled proportion is calculated by giving each sample proportion an equal weight.

Question 18

When using independent samples to test the difference between two population means,it is desirable but not necessary for the sample sizes to be the same.

Question 19

The F test is used to test for the equality of two population variances.

Question 20

When the variances are known,a test comparing two independent sample means would use the normal distribution.

Question 21

John wants to compare two means.His sample statistics were 1 = 22.7,s12 = 5.4,n1 = 9 and 2 = 20.5,s22 = 3.6,n2 = 9.Assuming equal variances,which is the approximate 95 percent confidence interval for the difference of the population means?

A)[2.44,6.19]
B)[1.17,5.08]
C)[0.08,4.32]
D)[−0.09,3.19]

Question 22

In a test for equality of two proportions,the sample proportions were p1 = 12/50 and p2 = 18/50.The test statistic is

A)−1.44
B)−1.31
C)−1.67
D)Impossible to determine without knowing α.

Question 23

If the sample proportions are p1 = 6/90 and p2 =4/100,normality may be assumed in a test comparing the two population proportions.

Question 24

If the population variances are exactly equal,the sample F test statistic will be zero.

Question 25

Kate wants to compare two means.Her sample statistics were 1 = 22.7,s12 = 5.4,n1 = 9 and 2 = 20.5,s22 = 3.6,n2 = 9.Assuming equal variances,the degrees of freedom for his test will be

A)16
B)18
C)9
D)8

Question 26

In a right-tailed test comparing two means with known variances,the sample sizes were n1 = 8 and n2 = 12.At α = .05,the critical value would be

A)1.960
B)1.645
C)1.734
D)1.282

Question 27

When the variances are unknown,a test comparing two independent sample means would use the Student's t distribution.

Question 28

If the sample proportions are p1 = 15/60 and p2 = 20/90,normality may be assumed in a test comparing the two population proportions.

Question 29

In a right-tailed test comparing two proportions,the test statistic was zcalc = +1.81.The p-value is

A).9649
B).0351
C).4649
D)Must know n to answer.

Question 30

In a left-tailed test comparing two means with variances unknown but assumed to be equal,the sample sizes were n1 = 8 and n2 = 12.At α = .05,the critical value would be

A)−1.960
B)−2.101
C)−1.734
D)−1.645

Question 31

A paired t-test with two columns of 8 observations in each column would use d.f.= 7.

Question 32

In a random sample of patient records in Cutter Memorial Hospital,six-month postoperative exams were given in 90 out of 200 cases,while in Paymor Hospital such exams were given in 110 out of 200 cases.The pooled proportion is

A).50
B).40
C).30
D).20

Question 33

In a left-tailed test comparing two means with unknown variances assumed to be equal,the test statistic was t = −1.81 with sample sizes of n1 = 8 and n2 = 12.The p-value would be

A)between .025 and .05.
B)between .01 and .025.
C)between .05 and .10.
D)Must know α to answer.

Question 34

In a random sample of patient records in Cutter Memorial Hospital,six-month postoperative exams were given in 90 out of 200 prostatectomy patients,while in Paymor Hospital such exams were given in 110 out of 200 cases.In a left-tailed test for equality of proportions,the p-value is

A).9772
B).0228
C).4772
D).0517

Question 35

Kate wants to compare two means.Her sample statistics were 1 = 22.7,s12 = 5.4,n1 = 9 and 2 =20.5,s22 = 3.6,n2 = 9 .Assuming equal variances,the pooled variance is

A)4.5
B)4.9
C)5.1
D)3.8

Question 36

Management of Melodic Kortholt Company compared absenteeism rates in two plants on the third Monday in November.Of Plant A's 800 employees,120 were absent.Of Plant B's 1200 employees,144 were absent.To compare the two proportions,the pooled proportion is

A).130
B).140
C).132
D).135

Question 37

In a test for equality of two proportions,the sample proportions were p1 = 12/50 and p2 = 18/50.The pooled proportion is

A).20
B).24
C).36
D).30

Question 38

In a random sample of patient records in Cutter Memorial Hospital,six-month postoperative exams were given in 90 out of 200 prostatectomy patients,while in Paymor Hospital such exams were given in 110 out of 200 cases.In a left-tailed test for equality of proportions,the test statistic is

A)−1.96
B)−2.00
C)−4.00
D)−3.48

Question 39

If the sample proportions were p1 = 12/50 and p2 = 18/50,what is the approximate 95 percent confidence interval for the difference of the population proportions?

A)[−.144,+.244]
B)[−.120,+.120]
C)[−.298,+.058]
D)[−.011,.214]

Question 40

In a random sample of patient records in Cutter Memorial Hospital,six-month postoperative exams were given in 90 out of 200 prostatectomy patients,while in Paymor Hospital such exams were given in 110 out of 200 cases.In comparing these two proportions,normality of the difference may be assumed because

A)the populations are large enough to be assumed normal.
B)the probability of success can reasonably be assumed constant.
C)the samples are random,so the proportions are unbiased estimates.
D)nπ ≥ 10 and n(1 − π)≥ 10 for each sample taken separately.

Question 41

Two well-known aviation training schools are being compared using random samples of their graduates.It is found that 70 of 140 graduates of Fly-More Academy passed their FAA exams on the first try,compared with 104 of 260 graduates of Blue Yonder Institute.To compare the pass rates,the pooled proportion would be

A).500
B).435
C).400
D).345

Question 42

Of 200 youthful gamers (under 18)who tried the new Z-Box-Plus game,160 rated it "excellent," compared with only 144 of 200 adult gamers (18 or over).The p-value for a right-tailed test to compare the two proportions would be approximately

A).042
B).031
C).054
D).095

Question 43

Of 200 youthful gamers (under 18)who tried the new Z-Box-Plus game,160 rated it "excellent," compared with only 144 of 200 adult gamers (18 or over).The test statistic to test the two proportions for equality would be

A)1.645
B)1.960
C)1.873
D)1.448

Question 44

A new policy of "flex hours" is proposed.Random sampling showed that 28 of 50 female workers favored the change,while 22 of 50 male workers favored the change.Management wonders if there is a difference between the two groups.What is the test statistic to test for a zero difference in the population proportions?

A)1.321
B)1.287
C)1.200
D)−1.255

Question 45

Two well-known aviation training schools are being compared using random samples of their graduates.It is found that 70 of 140 graduates of Fly-More Academy passed their FAA exams on the first try,compared with 104 of 260 graduates of Blue Yonder Institute.To compare the pass rates,find the critical value for a right-tailed test at α = .05.

A)1.960
B)1.645
C)2.326

Question 46

Two well-known aviation training schools are being compared using random samples of their graduates.It is found that 70 of 140 graduates of Fly-More Academy passed their FAA exams on the first try,compared with 104 of 260 graduates of Blue Yonder Institute.To compare the two proportions,the assumption of normality of the test statistic is

A)justified,but it is a borderline case.
B)clearly justified.
C)clearly not justified.

Question 47

Carver Memorial Hospital's surgeons have a new procedure that they think will decrease the time to perform an appendectomy.A sample of 8 appendectomies using the old method had a mean of 38 minutes with a variance of 36 minutes,while a sample of 10 appendectomies using the experimental method had a mean of 29 minutes with a variance of 16 minutes.For a right-tailed test for equal means (assume equal variances),the critical value at α = .10 is

A)1.746
B)1.337
C)2.120
D)2.754

Question 48

At Huge University,a sample of 200 business school seniors showed that 26 planned to pursue an MBA degree,compared with 120 of 800 arts and sciences seniors.We want to know if the proportion is higher in the arts and sciences group.For this test,the assumption of normality for the difference of proportions is

A)clearly unjustified.
B)clearly justified.
C)a borderline call.

Question 49

Two well-known aviation training schools are being compared using random samples of their graduates.It is found that 70 of 140 graduates of Fly-More Academy passed their FAA exams on the first try,compared with 104 of 260 graduates of Blue Yonder Institute.The test statistic to test the pass rates for equality is

A)2.141
B)1.298
C)1.227
D)1.924

Question 50

Of 200 youthful gamers (under 18)who tried the new Z-Box-Plus game,160 rated it "excellent," compared with only 144 of 200 adult gamers (18 or over).The pooled proportion for a test to compare the two proportions would be

A).76
B).72
C).77
D)Must know α to answer.

Question 51

Of 200 youthful gamers (under 18)who tried the new Z-Box-Plus game,160 rated it "excellent," compared with only 144 of 200 adult gamers (18 or over).Calculate the 95 percent confidence interval for the difference of proportions.

A)[+.013,+.263]
B)[−.014,+.188]
C)[−.003,+.163]
D)[+.057,+.261]

Question 52

At Huge University,a sample of 200 business school seniors showed that 26 planned to pursue an MBA degree,compared with 120 of 800 arts and sciences seniors.We want to know if the proportion is higher in the arts and sciences group.The p-value for a left-tailed test is approximately

A).38
B).48
C).24
D).51

Question 53

Two well-known aviation training schools are being compared using random samples of their graduates.It is found that 70 of 140 graduates of Fly-More Academy passed their FAA exams on the first try,compared with 104 of 260 graduates of Blue Yonder Institute.In a right-tailed test,the p-value is .0274,so at α = .025 we should

A)reject the hypothesis of equal proportions.
B)not reject the hypothesis of equal proportions.
C)change the α to .05 to get a rejection.

Question 54

A new policy of "flex hours" is proposed.Random sampling showed that 28 of 50 female workers favored the change,while 22 of 50 male workers favored the change.Management wonders if there is a difference between the two groups.For a test comparing the two proportions,the assumption of normality for the difference of proportions is

A)clearly justified.
B)clearly unjustified.
C)a borderline call.

Question 55

A new policy of "flex hours" is proposed.Random sampling showed that 28 of 50 female workers favored the change,while 22 of 50 male workers favored the change.Management wonders if there is a difference between the two groups.What is the p-value for a two-tailed test?

A).3849
B).1151
C).2301
D).3453

Question 56

At Huge University,a sample of 200 business school seniors showed that 26 planned to pursue an MBA degree,compared with 120 of 800 arts and sciences seniors.We want to know if the proportion is higher in the arts and sciences group.The pooled proportion for this test is

A).130
B).140
C).145
D).146

Question 57

Management of Melodic Kortholt Company compared absenteeism rates in two plants on the third Monday in November.Of Plant A's 800 employees,120 were absent.Of Plant B's 1200 employees,144 were absent.MegaStat's results for a two-tailed test are shown below. At α = .05,the two-tailed test for a difference in proportions is

A)just barely significant.
B)not quite significant.
C)not feasible due to nonnormality.

Question 58

Management of Melodic Kortholt Company compared absenteeism rates in two plants on the third Monday in November.Of Plant A's 800 employees,120 were absent.Of Plant B's 1200 employees,144 were absent.MegaStat's results for a two-tailed test are shown below. The test statistic (shown as z = x.xx)is approximately

A)2.022
B)1.960
C)1.942
D)1.645

Question 59

Two well-known aviation training schools are being compared using random samples of their graduates.It is found that 70 of 140 graduates of Fly-More Academy passed their FAA exams on the first try,compared with 104 of 260 graduates of Blue Yonder Institute.To compare the pass rates,the p-value for a right-tailed test is approximately

A).054
B).027
C).155
D).013

Question 60

At Huge University,a sample of 200 business school seniors showed that 26 planned to pursue an MBA degree,compared with 120 of 800 arts and sciences seniors.We want to know if the proportion is higher in the arts and sciences group.What is the z test statistic?

A)−1.322
B)−1.122
C)−0.716
D)We must first know α.

Question 61

A random sample of Ersatz University students revealed that 16 females had a mean of $22.30 in their wallets with a standard deviation of $3.20,while 16 males had a mean of $17.30 with a standard deviation of $9.60.In comparing the population variances at α = .10 in a two-tailed test,we conclude that

A)the variances are equal.
B)the variances are unequal.
C)the variances are incomparable (different sample sizes).

Question 62

A psychology researcher has a theory that predicts women will tend to carry more cash than men.A random sample of Ersatz University students revealed that 16 females had a mean of $22.30 in their wallets with a standard deviation of $3.20,while 16 males had a mean of $17.30 with a standard deviation of $9.60.The researcher's hypothesis would lead us to perform a

A)right-tailed test.
B)left-tailed test.
C)two-tailed test.

Question 63

A psychology researcher has a theory that predicts women will tend to carry more cash than men.A random sample of Ersatz University students revealed that 16 females had a mean of $22.30 in their wallets with a standard deviation of $3.20,while 16 males had a mean of $17.30 with a standard deviation of $9.60.The test statistic for the researcher's hypothesis is

A)impossible to determine without knowing α.
B)1.250
C)1.504
D)1.976

Question 64

During a test period,an experimental group of 10 vehicles using an 85 percent ethanol-gasoline mixture showed mean CO2 emissions of 667 pounds per 1000 miles,with a standard deviation of 20 pounds.A control group of 14 vehicles using regular gasoline showed mean CO2 emissions of 679 pounds per 1000 miles with a standard deviation of 15 pounds.At α = .05,in a left-tailed test (assuming equal variances)the test statistic is

A)−1.310
B)−2.042
C)−1.645
D)−1.683

Question 65

Mary analyzed occupancy rates at two community hospitals and obtained the following Excel results. Which conclusion is correct in a two-tailed test at α = .05?

A)There appears to be no difference in the mean occupancy rates.
B)HealthPro has a significantly higher mean occupancy rate.
C)There is a significant difference in the mean occupancy rates.

Question 66

Carver Memorial Hospital's surgeons have a new procedure that they think will decrease the time to perform an appendectomy.A sample of 8 appendectomies using the old method had a mean of 38 minutes with a variance of 36 minutes,while a sample of 10 appendectomies using the experimental method had a mean of 29 minutes with a variance of 16 minutes.For a right-tailed test of equal means (assume equal variances),the pooled variance is

A)14.76
B)26.00
C)24.75
D)27.54

Question 67

Nacirema Airlines is buying a fleet of new fuel-efficient planes.The HogJet and the LitheJet both meet their price and performance needs,and both planes meet EPA noise guidelines.However,the quieter plane is preferred.Each plane is flown through a typical takeoff and landing sequence 10 times,while remote sensors at ground level record the noise levels (in decibels).The table below summarizes the sound level tests using Excel's default level of significance (α = .05). After inspecting this table,we would most likely

A)use the test assuming unequal variances.
B)use the test for equal variances.
C)perform another test to determine if the variances are equal before proceeding.
D)realize that the decision is not affected by our assumptions concerning the variance.

Question 68

Carver Memorial Hospital's surgeons have a new procedure that they think will decrease the time to perform an appendectomy.A sample of 8 appendectomies using the old method had a mean of 38 minutes with a variance of 36 minutes,while a sample of 10 appendectomies using the experimental method had a mean of 29 minutes with a variance of 16 minutes.For a right-tailed test of means (assume equal variances),the test statistic is

A)3.814
B)2.365
C)3.000
D)1.895

Question 69

Mary did an analysis of acute care variances in samples of occupancy rates at two community hospitals and obtained the following results: Can Mary conclude that the variances are unequal at α = 0.05?

A)No,there is not enough evidence to believe the variances are unequal.
B)Yes,the analysis shows that the variances are unequal.
C)You cannot tell without knowing the sample sizes.

Question 70

Based on a random sample of 13 tire changes,the mean time to change a tire on a Boeing 777 has a mean of 59.5 minutes with a standard deviation of 8.4 minutes.For 10 tire changes on a Boeing 787,the mean time was 64.3 minutes with a standard deviation of 12.4 minutes.To test for equal variances in a two-tailed test at α = .10,the critical values are

A)3.73 and 0.228
B)2.51 and 3.67
C)3.07 and 0.398
D)3.07 and 0.357

Question 71

During a test period,an experimental group of 10 vehicles using an 85 percent ethanol-gasoline mixture showed mean CO2 emissions of 240 pounds per 100 miles,with a standard deviation of 20 pounds.A control group of 14 vehicles using regular gasoline showed mean CO2 emissions of 252 pounds per 100 miles with a standard deviation of 15 pounds.A quick comparison of the sample variances suggests that the population variances are

A)probably equal.
B)probably unequal.
C)incomparable.

Question 72

Nacirema Airlines is buying a fleet of new fuel-efficient planes.The HogJet and the LitheJet both meet their price and performance needs,and both planes meet EPA noise guidelines.However,the quieter plane is preferred.Each plane is flown through a typical takeoff and landing sequence 10 times,while remote sensors at ground level record the noise levels (in decibels).The table below summarizes the sound level tests using Excel's default level of significance (α = .05). In a left-tailed test comparing the means at α = .05,we would

A)not reject H0.
B)reject H0.
C)have insufficient information to make a decision.

Question 73

Nacirema Airlines is buying a fleet of new fuel-efficient planes.The HogJet and the LitheJet both meet their price and performance needs,and both planes meet EPA noise guidelines.However,the quieter plane is preferred.Each plane is flown through a typical takeoff and landing sequence 10 times,while remote sensors at ground level record the noise levels (in decibels).The table below summarizes the sound level tests using Excel's default level of significance (α = .05). If we switched from α = 0.05 to α = 0.005 in a two-tailed test of means,our assumption about variances (assumed equal or assumed unequal)would

A)affect the decision.
B)not affect the decision.
C)require a new analysis.

Question 74

A certain psychological theory predicts that men want bigger families than women.Kate asked each student in her psychology class how many children he or she considered ideal for a married couple and obtained the Excel results shown below at α = .05. What conclusion can you draw in a two-tailed test at α = .05?

A)Men want larger families on average than women.
B)Women want larger families on average than men.
C)We cannot reject the hypothesis of equal population means.
D)The decision depends on whether or not the variances are equal.

Question 75

Randomly chosen MBA students were asked their opinions about the ideal number of children for a married couple.The sample data were entered into MegaStat,and the following results were produced. What conclusion can you draw from this analysis at α = .05?

A)Men want larger families on average than women.
B)Women want larger families on average than men.
C)This is insufficient evidence to suggest a difference in means.
D)We could conclude that men want larger families if we used a two-tailed test.

Question 76

During a test period,an experimental group of 10 vehicles using an 85 percent ethanol-gasoline mixture showed mean CO2 emissions of 667 pounds per 1000 miles,with a standard deviation of 20 pounds.A control group of 14 vehicles using regular gasoline showed mean CO2 emissions of 679 pounds per 1000 miles with a standard deviation of 15 pounds.Assuming equal variances,the pooled variance is

A)296.59
B)225.00
C)400.00
D)522.16

Question 77

During a test period,an experimental group of 10 vehicles using an 85 percent ethanol-gasoline mixture showed mean CO2 emissions of 667 pounds per 1000 miles,with a standard deviation of 20 pounds.A control group of 14 vehicles using regular gasoline showed mean CO2 emissions of 679 pounds per 1000 miles with a standard deviation of 15 pounds.At α = .05,in a left-tailed test,the critical value to compare the means (assuming equal variances)is

A)−2.508
B)−2.074
C)−1.321
D)−1.717

Question 78

Litter sizes (number of pups)for randomly chosen dogs from two breeds were compared.The sample data were entered into Excel,and the following results were produced. What is the p-value for a left-tailed test comparing the means at α = .05?

A)Less than .10
B)More than .10
C)Between .10 and .05
D)Between .05 and .01

Question 79

Randomly chosen MBA students were asked their opinions about the ideal number of children for a married couple.The sample data were entered into MegaStat,and the following results were produced. To compare the means,would it be appropriate to use a test that assumes equal variances?

A)Yes,because by pooling our variances,we can simplify our calculations.
B)Yes,we should assume equal variances when comparing independent samples.
C)No,because the sample statistics show that the variances are unequal at α = 0.05.
D)No,because the variances will differ because the means differ significantly.

Question 80

Litter sizes (number of pups)for randomly chosen dogs from two breeds were compared.The sample data were entered into Excel,and the following results were produced. What is the critical value for a left-tailed test comparing the means at α = 0.05?

A)−1.645
B)−1.721
C)−1.703
D)−1.699