Deck 10: The T Test for Two Independent Samples

Question 1

Two samples, each with n = 6 subjects, produce a pooled variance of 20.Based on this information, what is the estimated standard error for the sample mean difference?

A)20/6
B)20/12
C)the square root of (20/6 + 20/6)
D)the square root of (20/5 + 20/5)

Answer 1

C

Question 2

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)n = 15
B)n = 16
C)n = 30
D)n = 31

Answer 2

B

Question 3

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/ $\surd$ 2
D)4/ $\surd$ 8

Answer 3

2

Question 4

The data from an independent-measures research study produce a sample mean difference of 4 points and a pooled variance of 16.If there are n = 8 scores in each sample, then what is the estimated standard error for the sample mean difference?

A)2
B)4
C)16
D)128

Question 5

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 6

In an independent-measures hypothesis test, what must be true if t = 0?

A)The two population means must be equal.
B)The two sample means must be equal.
C)The two sample variances must be equal.
D)None of the other 3 choices is correct.

Question 7

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, then the value for the t statistic is _____.

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

Question 8

One sample of n = 8 scores has a variance of s² = 6 and a second sample of n = 8 scores has 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 half way between 6 and 10
D)cannot be determined without more information

Question 9

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 10

Which of the following accurately describes an independent-measures study?

A)It uses a different group of participants for each of the treatment conditions being compared.
B)It uses the same group of participants in all of the treatment conditions being compared.
C)It uses one group of participants to evaluate a hypothesis about one population mean.
D)none of the other alternatives is correct

Question 11

An independent-measures research study uses two samples, each with n = 12 participants.If the data produce a t statistic of t = 2.08, then 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)Fail to reject the null hypothesis with either α = .05 or α = .01.
B)Reject the null hypothesis with either α = .05 or α = .01.
D)Cannot answer without additional information

Question 12

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

Question 13

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 EQ \O(=,/) 0
D)M₁ - M₂ EQ \O(=,/) 0

Question 14

An independent-measures study has one sample with n = 10 and a second sample with n = 15 to compare two experimental treatments.What is the df value for the t statistic for this study?

A)23
B)24
C)26
D)27

Question 15

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 half way between 20 and 30.
D)Cannot be determined without more information.

Question 16

An independent-measures study uses two samples, each with n = 10, to compare two treatment conditions.What is the df value for the t statistic for this study?

A)8
B)9
C)18
D)19

Question 17

One sample has a variance of s² = 10 and a second sample has a variance of s² = 6.If the two samples have the same number of scores, what is the pooled variance for the two samples?

A)4
B)8
C)14
D)Cannot answer without knowing the sample size.

Question 18

An independent-measures research study uses two samples, each with n = 12 participants.If the data produce a t statistic of t = 2.50, then 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 19

What is the pooled variance for the following two samples?

Question 20

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

A)the square root of (30/15)
B)the square root of (60/15)
C)the square root of (30/5 + 30/10)
D)the square root of (30/4 + 30/9)

Question 21

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

A)The two sample means are 10 and 12 with sample variances of 20 and 25.
B)The two sample means are 10 and 12 with variances of 120 and 125.
C)The two sample means are 10 and 20 with variances of 20 and 25.
D)The two sample means are 10 and 20 with variances of 120 and 125.

Question 22

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 23

The results of an independent-measures research study are reported as "t(20) = 2.12, p < .05, two tails." For this study, what t values formed the boundaries for the critical region?

A)±2.093
B)±2.086
C)±2.080
D)±2.074

Question 24

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

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

Question 25

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 26

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 27

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 28

If n = 15 for each sample, which of the following sets of data provides the clearest difference between the two samples?

A)a sample mean difference of 5 points with s² = 5 for both samples
B)a sample mean difference of 5 points with s² = 10 for both samples
C)a sample mean difference of 10 points with s² = 5 for both samples
D)a sample mean difference of 10 points with s² = 10 for both samples

Question 29

For an independent-measures research study, the data show an 8-point difference between the two treatment means and a pooled variance of 4.Given this information, what is the value of Cohen's d?

A)8/4
B)8/2
C)4/8
D)Cannot answer without knowing the sample sizes.

Question 30

For an independent-measures research study, what is measured by Cohen's d or r²?

A)the risk of a Type I error
B)the risk of a Type II error
C)the size of the difference between the two treatments
D)whether the difference between the two treatments is likely to have occurred by chance

Question 31

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 32

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

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 33

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 34

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 35

An independent-measures study produces sample means of M₁ = 35 and M₂ = 31 and a pooled variance of 25.For this study, Cohen's d = ______.

A)d = 4/25
B)d = 25/4
C)d = 4/5
D)d = 5/4

Question 36

Assuming that there is 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 37

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, you can conclude that the difference between the two sample means is _____.

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

Question 38

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 39

One sample has M = 18 and a second sample has M = 14.If the pooled variance for the two samples is 16, then 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 40

If the sample mean difference is 3 points, which of the following sets of data would produce the largest value for Cohen's d?

A)n = 10 for both samples and a pooled variance of 15
B)n = 20 for both samples and a pooled variance of 15
C)n = 30 for both samples and a pooled variance of 15
D)Cohen's d is the same for all three of the samples.

Question 41

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

Question 42

If the df value for an independent-measures t statistic is an odd number, then it is impossible for the two samples to be the same size.

Question 43

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

Question 44

For an independent-measures t statistic, the estimated standard error measures how much difference is reasonable to expect between the two sample means if the null hypothesis is true.

Question 45

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 46

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

Question 47

Two separate samples, each with n = 10 scores, will produce an independent-measures t statistic with df = 19.

Question 48

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

Question 49

If other factors are held constant, the larger the difference between the two sample means is, the larger the value for the independent-measures t statistic will be.

Question 50

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

Question 51

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 52

If two samples each have s² = 10, then the pooled variance will be equal to 20.

Question 53

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 for samples selected from the same population.

Question 54

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 55

The null hypothesis for the independent-measures t test states that there is no difference between the two sample means.

Question 56

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

Question 57

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

Question 58

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

Question 59

The results from an independent-measures t hypothesis test are reported as "t(14) = 2.13,
p > .05, two tailed." For this test, the null hypothesis was rejected.

Question 60

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 61

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

Question 62

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 26 subjects.

Question 63

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 64

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 65

An independent-measures study produces t(21) = 3.00, p < .01.For this study, if effect size is measured with r², then r² = 9/30.

Question 66

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

Question 67

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 68

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 69

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

Question 70

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