Deck 10: The t Test for Two Independent Samples

Question 1

An independent-measures study comparing two treatment conditions produces a t statistic with df = 18.If the two samples are the same size,how many participants were in each of the samples?

A)9
B)10
C)19
D)20

Answer 1

10

Question 2

One sample has a variance of s² = 10 and a second sample has a variance of s² = 6.Which of the following most accurately describes the pooled variance for the two samples?

A)Closer to 6 than to 10
B)Closer to 10 than to 6
C)Somewhere between 6 and 10
D)Around 16

Answer 2

Somewhere between 6 and 10

Question 3

An independent-measures research study uses a total of 40 participants to compare two treatment conditions.What is the df value for the t statistic for this study?

A)18
B)19
C)38
D)39

Answer 3

38

Question 4

One sample of n = 8 scores has a variance of s² = 6 and a second sample of n = 8 scores has a variance of s² = 10.If the pooled variance is computed for these two samples,then the value obtained will be ______.

A)closer to 6 than to 10
B)closer to 10 than to 6
C)exactly halfway between 6 and 10
D)cannot be determined without more information

Question 5

Which of the following is the correct null hypothesis for an independent-measures t test?

A)μ1 - μ2 = 0
B)M1 - M2 = 0
C)μ1 - μ2 ≠ 0
D)M1 - M2 ≠ 0

Question 6

Which of the following research situations would be most likely to use an independent-measures design?

A)Examine the development of vocabulary as a group of children mature from age 2 to age 3.
B)Examine the long-term effectiveness of a stop-smoking treatment by interviewing subjects 2 months and 6 months after the treatment ends.
C)Compare the mathematics skills for 9th-grade boys versus 9th-grade girls.
D)Compare the blood-pressure readings before medication and after medication for a group a patients with high blood pressure.

Question 7

A researcher reports an independent-measures t statistic with df = 16.How many participants were in the entire study?

A)17
B)18
C)33
D)34

Question 8

The data from an independent-measures research study produce a sample mean difference of 4 points and a pooled variance of 18.If there are n = 4 scores in each sample,what is the estimated standard error for the sample mean difference?

A)3
B)9
C)12
D)The square root of 12

Question 9

Two samples,each with n = 5 scores,have a pooled variance of 40.What is the estimated standard error for the sample mean difference?

A)4
B)8
C)10
D)20

Question 10

An independent-measures study uses n = 15 participants in each group to compare two treatment conditions.What is the df value for the t statistic for this study?

A)14
B)15
C)28
D)29

Question 11

Two samples each have n = 4 scores.If the first sample has a variance of 10 and the second sample has a variance of 6,what is the estimated standard error for the sample mean difference?

A)1
B)2
C)4
D)Cannot determine without more information

Question 12

What is the pooled variance for the following two samples?

A)7 Sample 1: n = 8 and SS = 168
B)√7 Sample 2: n = 6 and SS = 120
C)20.57
D)24

Question 13

A researcher reports an independent-measures t statistic with df = 30.If the two samples are the same size (n₁ = n₂),then how many individuals are in each sample?

A)15
B)16
C)30
D)31

Question 14

An independent-measures study has one sample with n = 6 and a second sample with n = 8 to compare two experimental treatments.What is the df value for the t statistic for this study?

A)7
B)12
C)13
D)14

Question 15

If an independent-measures design is being used to compare two treatment conditions,then how many different groups of participants would be needed and how many scores would there be for each participant?

A)1 group, 1 score each
B)2 groups, 1 score each
C)1 group, 2 scores each
D)2 groups, 2 scores each

Question 16

One sample has n = 10 scores and a variance of s² = 20,and a second sample has n = 15 scores and a variance of s² = 30.What can you conclude about the pooled variance for these two samples?

A)It will be closer to 20 than to 30.
B)It will be closer to 30 than to 20.
C)It will be exactly halfway between 20 and 30.
D)Cannot be determined without more information.

Question 17

Two samples,each with n = 16 scores,produce an estimated standard error of 4 points and a t statistic of t = 2.00.What is the sample mean difference?

A)2
B)4
C)8
D)16

Question 18

One sample has n = 5 scores and the second has n = 10 scores.If the pooled variance for the two samples is 30,what is the value of the estimated standard error for the sample mean difference?

A)2
B)√2
C)9
D)3

Question 19

An independent-measures study with n = 6 in each sample produces a sample mean difference of 4 points and a pooled variance of 12.What is the value for the t statistic?

A)1
B)2
C)4/√2
D)4/√8

Question 20

The data from an independent-measures research study produce a sample mean difference of 6 points and an estimated standard error of 2 points.If there are n = 8 scores in each sample,what is the value for the t statistic?

A)6/2
B)6/4
C)6/0.25
D)6/0.50

Question 21

What is the average value expected for the independent-measures t statistic if the null hypothesis is true?

A)0
B)1
C)±1
D)M1 - M2

Question 22

Which of the following confidence intervals also indicates a significant difference between treatments with α = .05?

A)Estimate that μ1 - μ2 is in an interval between 2 and 10 with 90% confidence
B)Estimate that μ1 - μ2 is in an interval between -2 and 8 with 90% confidence
C)Estimate that μ1 - μ2 is in an interval between 2 and 10 with 95% confidence
D)Estimate that μ1 - μ2 is in an interval between -2 and 8 with 95% confidence

Question 23

Two separate samples are being used to estimate the population mean difference between two treatment conditions.Which of the following would produce the widest confidence interval?

A)n1 = n2 = 10 with a pooled variance of 10
B)n1 = n2 = 10 with a pooled variance of 100
C)n1 = n2 = 20 with a pooled variance of 10
D)n1 = n2 = 20 with a pooled variance of 100

Question 24

For the independent-measures t statistic,what is the effect of increasing the sample variances?

A)Increase the likelihood of rejecting H0 and increase measures of effect size
B)Increase the likelihood of rejecting H0 and decrease measures of effect size
C)Decrease the likelihood of rejecting H0 and increase measures of effect size
D)Decrease the likelihood of rejecting H0 and decrease measures of effect size

Question 25

One sample has M = 18 and a second sample has M = 14.If the pooled variance for the two samples is 16,what is the value of Cohen's d?

A)0.25
B)0.50
C)1.00
D)Cannot be determined with the information given

Question 26

An independent-measures research study uses two samples,each with n = 15 participants.If the data produce a t statistic of t = 2.760,which of the following is the correct decision for a two-tailed hypothesis test?

A)Reject the null hypothesis with α = .05 but fail to reject with α = .01
B)Reject the null hypothesis with either α = .05 or α = .01
C)Fail to reject the null hypothesis with either α = .05 or α = .01
D)Cannot answer without additional information

Question 27

A researcher reports t(22)= 5.30,p < .01 for an independent-measures experiment.How many individuals participated in the entire experiment?

A)20
B)21
C)23
D)24

Question 28

The results of an independent-measures research study are reported as "t(22)= 2.12,p < .05,two tails." For this study,what t values formed the boundaries for the critical region?

A)±2.080
B)±2.074
C)±2.069
D)±2.064

Question 29

A researcher predicts that scores in treatment A will be higher than scores in treatment B.If the mean for the 10 participants in treatment A is 4 points higher than the mean for the 10 participants in treatment B and the data produce t = 2.095,what decision should be made?

A)With α = .05, reject H0 for both a one-tailed and a two-tailed test
B)With α = .05, fail to reject H0 for both a one-tailed and a two-tailed test
C)With α = .05, reject H0 for a one-tailed test but fail to reject for a two-tailed test
D)With α = .05, reject H0 for a two-tailed test but fail to reject for a one-tailed test

Question 30

An independent-measures research study with n = 5 participants in each treatment produces sample variances of 8 and 10,and a 2-point difference between the two treatment means.What is the value of Cohen's d?

A)2/2
B)2/3
C)2/9
D)2/18

Question 31

An independent-measures study produces sample means of M₁ = 20 and M₂ = 17.If both samples have n = 18 scores and Cohen's d = 0.50,what is the value for the pooled variance?

A)2
B)4
C)6
D)36

Question 32

Two samples,each with n = 8,produce an independent-measures t statistic of t = -2.15.Which of the following decisions is justified for a two-tailed test?

A)Reject H0 with α = .05 but fail to reject with α = .01
B)Reject H0 with both α = .05 and α = .01
C)Fail to reject H0 with both α = .05 and α = .01
D)Fail to reject H0 with α = .05 but reject H0 with α = .01

Question 33

An independent-measures study produces sample means of M₁ = 20 and M₂ = 17,and a pooled variance of 9.For this study,what is the value of Cohen's d?

A)3/3
B)3/9
C)3
D)Impossible to determine without knowing the sample sizes

Question 34

An independent-measures study comparing two treatment conditions with n = 6 in each sample produces t = 4.00.What is the value of r² for this study?

A)4/26
B)4/28
C)16/26
D)16/28

Question 35

A researcher predicts that scores in treatment A will be higher than scores in treatment B.Which of the following is the correct null hypothesis for a one-tailed test evaluating this prediction?

A)µA = µB
B)µA / µB
C)µA > µB
D)µA < µB

Question 36

Using an independent-measures t,the 90% confidence interval for the difference between two population means ranges from 19 to 23.Based on this confidence interval,how big is the difference between the two sample means?

A)4 points
B)19 points
C)21 points
D)23 points

Question 37

Two samples,each with n = 9 scores,produce an independent-measures t statistic of t = 2.00.If the effect size is measured using r²,what is the value of r²?

A)4/16
B)4/20
C)2/16
D)2/18

Question 38

For the independent-measures t statistic,what is the effect of increasing the difference between sample means?

A)Increase the likelihood of rejecting H0 and increase measures of effect size
B)Increase the likelihood of rejecting H0 and decrease measures of effect size
C)Decrease the likelihood of rejecting H0 and increase measures of effect size
D)Decrease the likelihood of rejecting H0 and decrease measures of effect size

Question 39

The narrower the confidence interval,the more precise it is.With this in mind,which combination of factors will produce the most precise estimate of the difference between two population means?

A)Two samples of n = 20 and 80% confidence
B)Two samples of n = 20 and 90% confidence
C)Two samples of n = 50 and 80% confidence
D)Two samples of n = 50 and 90% confidence

Question 40

An independent-measures research study uses two samples,each with n = 10 participants.If the data produce a t statistic of t = 2.095,which of the following is the correct decision for a two-tailed hypothesis test?

A)Reject the null hypothesis with α = .05 but fail to reject with α = .01
B)Reject the null hypothesis with either α = .05 or α = .01
C)Fail to reject the null hypothesis with either α = .05 or α = .01
D)Cannot answer without additional information

Question 41

Assuming a 5-point difference between the two sample means,which set of sample characteristics is most likely to produce a significant value for the independent-measures t statistic?

A)Large sample sizes and small sample variances
B)Large sample sizes and large sample variances
C)Small sample sizes and small sample variances
D)Small sample sizes and large sample variances

Question 42

A research study compares the mean weight for a sample of n = 36 participants before they begin a 6-week diet and their mean weight at the end of the diet.This is an example of an independent-measures design.

Question 43

For an independent-measures t statistic,the estimated standard error measures how much difference is reasonable to expect between the sample means for two samples selected from the same population.

Question 44

One sample has s² = 12,and a second sample has s² = 15.The pooled variance for these two samples will be between 12 and 15.

Question 45

What is assumed by the homogeneity of variance assumption?

A)The two samples have equal variances.
B)The two sample variances are not equal.
C)The two populations have equal variances.
D)The two population variances are not equal.

Question 46

Which set of sample characteristics is most likely to produce a significant value for the independent-measures t statistic and a large effect size?

A)A small mean difference and small sample variances
B)A large mean difference and small sample variances
C)A small mean difference and large sample variances
D)A large mean difference and large sample variances

Question 47

If other factors are held constant,which of the following sets of data is most likely to satisfy the homogeneity of variance assumption?

A)A sample mean difference of 6 points and sample variances of 15 and 10
B)A sample mean difference of 4 points and sample variances of 9 and 6
C)A sample mean difference of 2 points and sample variances of 6 and 4
D)The other 3 options are equally likely to satisfy the assumption.

Question 48

If other factors are held constant,which of the following sets of data would produce the largest value for an independent-measures t statistic?

A)The two samples both have n = 15, with sample variances of 20 and 25.
B)The two samples both have n = 15, with variances of 120 and 125.
C)The two samples both have n = 30, with sample variances of 20 and 25.
D)The two samples both have n = 30, with variances of 120 and 125.

Question 49

For an independent-measures t statistic,you typically must compute the pooled variance before calculating the estimated standard error.

Question 50

If one sample has n = 5 scores with SS = 40 and a second sample has n = 5 scores with SS = 20,then the pooled variance will be 60/10 = 6.

Question 51

An independent-measures study with n = 20 scores in each treatment will produce an independent-measures t statistic with df = 19.

Question 52

If the two samples are the same size,then the pooled variance will equal the average of the two sample variances.

Question 53

If the two samples are the same size,the degrees of freedom for the independent measures t statistic will be an even number.

Question 54

For an independent-measures t statistic,what is the effect of increasing the number of scores in the samples?

A)Increase the likelihood of rejecting H₀ and increase measures of effect size
B)Increase the likelihood of rejecting H₀ and decrease measures of effect size
C)Increase the likelihood of rejecting H₀ and have little or no effect on measures of effect size
D)Decrease the likelihood of rejecting H₀ and have little or no effect on measures of effect size

Question 55

One sample has n = 7 scores with SS = 40,and a second sample has n = 5 scores with SS = 80.The pooled variance for these two samples is 120/10 = 12.

Question 56

If other factors are held constant,which of the following sets of data is most likely to produce a significant mean difference?

A)A sample mean difference of 5 points with n = 5 for both samples
B)A sample mean difference of 5 points with n = 10 for both samples
C)A sample mean difference of 10 points with n = 5 for both samples
D)A sample mean difference of 10 points with n = 10 for both samples

Question 57

Which of the following sets of data would produce the largest value for Cohen's d?

A)n = 10 for both samples, a pooled variance of 15, and a mean difference of 3 points
B)n = 20 for both samples, a pooled variance of 15, and a mean difference of 5 points
C)n = 10 for both samples, a pooled variance of 20, and a mean difference of 3 points
D)n = 20 for both samples, a pooled variance of 20, and a mead difference of 5 points

Question 58

Which of the following sets of data would produce the largest value for an independent-measures t statistic?

A)Sample means of 10 and 12, with sample variances of 20 and 25.
B)Sample means of 10 and 12, with sample variances of 120 and 125.
C)Sample means of 10 and 20, with sample variances of 20 and 25.
D)Sample means of 10 and 20, with sample variances of 120 and 125.

Question 59

If both samples have the same number of scores (n),then the independent-measures t statistic will have df = 2n - 2.

Question 60

Which combination of factors is most likely to produce a significant value for an independent-measures t statistic?

A)Large samples and large variance
B)Large samples and small variance
C)Small samples and large variance
D)Small samples and small variance

Question 61

An independent-measures research study uses a total of 18 participants to compare two treatment conditions.If the results are used to construct a 90% confidence interval for the population mean difference,then the t values will be ±1.746.

Question 62

The 95% confidence interval for the difference between two treatment means extends from 2.50 to +5.50.Based on this information,you can conclude that there is no significant difference between the treatments at the .05 level of significance.

Question 63

An independent-measures study produces t(10)= 3.00,p < .05.For this study,if effect size is measured with r²,then r² = 3/13.

Question 64

If two separate samples have M₁ = 10 and M₂ = 18 with a pooled variance of 16,then Cohen's d = 0.50.

Question 65

For a hypothesis test with the independent-measures t statistic,the null hypothesis states that the two population means are the same and the homogeneity assumption states that the two population variances are the same.

Question 66

When pooling variances,the resulting value will be closer to the variance for the sample with the smaller number of scores.

Question 67

If other factors are held constant,the larger the two sample sizes,the greater the likelihood that the independent-measures t test will find a significant difference.

Question 68

The homogeneity of variance assumption states that the two population variances are equal.

Question 69

If an independent-measures t statistic has df = 20,then a total of 18 individuals participated in the research study.

Question 70

An independent-measures study has M₁ = 49 and M₂ = 45 with an estimated standard error of 4.For this study,Cohen's d = 4/4 = 1.00.

Question 71

The results from an independent-measures t hypothesis test are reported as "t(24)= 3.85, p < .01,two tailed." The research study for this test used a total of 25 subjects.

Question 72

Two samples,each with n = 4 scores,have a pooled variance of 32.The estimated standard error for the sample mean difference is √8.

Question 73

If one sample has n = 4 and SS = 90 and a second sample has n = 8 and SS = 150,then the estimated standard error for the sample mean difference is 9 points.

Question 74

For an independent-measures study,the width of a confidence interval estimating µ₁ - µ₂ depends on the size of the difference between M₁ and M₂.

Question 75

If other factors are held constant,the larger the values for the two sample variances,the greater the likelihood that the independent-measures t test will find a significant difference.

Question 76

The results from an independent-measures t hypothesis test are reported as "t(14)= 2.10,
p > .05,two tailed." For this test,the null hypothesis was rejected.

Question 77

The estimated standard error for the independent-measures t statistic provides a measure of how much difference should exist,on average,between two sample means when the null hypothesis is true.

Question 78

If other factors are held constant,the larger the difference between the two sample means,the greater the likelihood that the independent-measures t test will find a significant difference.

Question 79

Confidence intervals with the independent-measures t statistic are used to estimate how much difference there is between two population means.

Question 80

If two sample variances are not equal,the pooled variance will be closer to the larger of the two variances.