Deck 10: The T Test for Two Independent Samples

Question 1

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)​16

Answer 1

​8

Question 2

What is the pooled variance for the following two samples?​Sample 1:n = 8 and SS = 168Sample 2:n = 6 and SS = 120

A)​7
B)​Ö7
C)​20.57
D)​24

Answer 2

​24

Question 3

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 3

​The square root of (20/6 + 20/6)

Question 4

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 5

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)​It will be equal to 25.

Question 6

A research design that uses a separate group of participants for each treatment condition(or for each population)is called an independent-measures research designor a____.​

A)​repeated-measures design
B)​dependent-measures design
C)​between-subjects design
D)​within-subjects design

Question 7

An independent-measures study uses ____.​

A)​a different group of participants for each of the treatment conditions being compared
B)​the same group of participants in all of the treatment conditions being compared
C)​one group of participants to evaluate a hypothesis about one population mean
D)​one individual to study andestimate population parameters

Question 8

​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 9

​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)​The two sample means are not equal.

Question 10

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 11

​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)​equal to 10

Question 12

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)​4/6
D)​4/8

Question 13

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 14

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 15

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)? $\sqrt { 20 }$

Question 16

​Researchers conduct a hypothesis test and use the data from two separate sets of observations drawn from the same group of participants.Their research design is called a repeated-measures research design or a(n)____.

A)​independent-measures design
B)​dependent-measures design
C)​between-subjects design
D)​within-subjects design

Question 17

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 18

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 19

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 20

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

Question 21

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 22

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)​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)​It cannot be answered without additional information.

Question 23

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 24

​Two samples,each with n = 9 scores,produce an independent-measures t statistic oft = 2.00.If the effect size is measured using r²,what is the value ofr²?

A)​4/16
B)​4/20
C)​2/16
D)​2/18

Question 25

​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 26

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 27

​Two separate samples are being used to estimate the difference between population means for 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 28

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)​8/1

Question 29

​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 30

​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 31

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)​4.00

Question 32

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 33

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 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

​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 36

​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)​It cannot be answered without additional information.

Question 37

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 38

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 39

​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 40

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 hypothesis test?​

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 41

The independent-measures t statistic uses the data from two separate samples to draw inferences about the mean difference between two populations or between two different treatment conditions.​

Question 42

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

Question 43

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

Question 44

​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 45

​One method for correcting the bias in the standard error is to "pool" the two sample variances using a procedure that allows the bigger sample to carry more weight in determining the final value of the variance.

Question 46

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 47

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

Question 48

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 49

?Two samples,each with n = 4 scores,have a pooled variance of 32.The estimated standard error for the sample mean difference is $\sqrt { 8 }$ .

Question 50

​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 51

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

Question 52

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

Question 53

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

Question 54

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

Question 55

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

Question 56

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 57

​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 58

​If two samples each have s² = 10,then the pooled variance will be equal to 20,regardless of sample size.

Question 59

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

Question 60

​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 61

The problems associated with high variance often can be minimized by transforming the original scores to ranks and then conducting an alternative statistical analysis known as the Mann-Whitney test.​

Question 62

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

Question 63

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 64

A major company would like to assess the impact of using a professional trainer to conduct a confidence-building workshop with their salespeople.A sample of 16 workers is obtained.Half (n = 8)attend the workshop and the other half (n = 8)serves as a control group.For the first group of salespeople who attending the training,M = 22.7 and SS = 100.For the second group of salespeople who did not attend the training,M = 17.5 and SS = 124.​Use the sample data to construct an 80% confidence interval for the mean difference in confidence between the control group and the workshop conditions.

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

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 67

​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 68

A researcher conducts an independent-measures study examining how the brain chemical serotonin is related to aggression.One sample of rats serves as a control group and receives a placebo that does not affect normal levels of serotonin.A second sample of rats receives a drug that lowers brain levels of serotonin.Then the researcher tests the animals by recording the number of aggressive responses each of the rats display.The data are as follows.
a. Does the drug have a significant effect on aggression? Use an alpha level of .05, two tails.
b. Compute Cohen's d to measure the size of the treatment effect.

Question 69

​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 70

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 71

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 72

The following data are from an independent-measures experiment comparing two treatmentconditions.​ ​
a. Does the data indicate a significant difference between the treatments at the .05 level of significance?
b. Compute r² to measure the size of the treatment effect.
c. Write a sentence demonstrating how the outcome of the hypothesis test and the measure of effect size would appear in a research report.​

Question 73

An educational psychologist studies the effect of frequent testing on retention of class material.In one section of an introductory course,students are given quizzes each week.A second section of the same course receives only two tests during the semester.At the end of the semester,both sections receive the same final exam,and the scores are summarized below.
a.If the first sample variance is s² = 38 and the second sample has s² = 42, do the data indicate that testing frequency has a significant effect on performance? Use a two-tailed test at the .05 level of significance.(Note: Because the two sample are the same size, the pooled variance is simply the average of the two sample variances.)
b.If the first sample variance is s² = 84 and the second sample has s² = 96, do the data indicate that testing frequency has a significant effect? Again, use a two-tailed test with α = .05.
c.Describe how the size of the variance affects the outcome of the hypothesis test.​

Question 74

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

Question 75

Describe the data that are collected for an independent-measures t test and the hypotheses that the test evaluates.​