Question 1

A researcher conducts a repeated-measures study to evaluate a treatment with a sample of n = 16 participants and obtains a t statistic of t = 1.94.The treatment is expected to increase scores and the sample mean shows an increase.Which of the following is the correct decision for a hypothesis test using α = .05.
A)Reject the null hypothesis with a one-tailed test but fail to reject with two tails
B)Reject the null hypothesis with either a one-tailed or a two-tailed test
C)Fail to reject the null hypothesis with either a one-tailed or a two-tailed test
D)Fail to reject the null hypothesis with a one-tailed test but reject with two tails

Accepted Answer

Since the researcher expects the treatment to increase scores and the sample mean shows an increase, the alternative hypothesis is one-tailed (i.e., the treatment increases scores). With a t-statistic of 1.94 and a sample size of 16, the degrees of freedom (df) is 15. Using a t-table, the critical values for a one-tailed test with α = .05 and df = 15 are t = 1.753 (for a lower-tailed test) and t = -1.753 (for an upper-tailed test). Since the obtained t-value of 1.94 falls in the critical region of the lower-tailed test, we reject the null hypothesis with a one-tailed test, but fail to reject it with a two-tailed test.

Question 2

In general,if the variance of the difference scores increases,what will happen to the value of the t statistic?
A)It will increase (move farther toward the tail of the distribution).
B)It will decrease (move toward 0 at the center of the distribution).
C)It will stay the same; the t statistic is not affected by the variance of the difference scores.
D)It may increase or may decrease; there is no consistent relationship between variance and the size of the t statistic.

Accepted Answer

The t statistic is inversely related to the variance of the difference scores. As variance increases, the standard error increases, leading to a decrease in the t statistic, moving it closer to 0.

Question 3

What value is estimated with a confidence interval using the repeated-measures t statistic?
A)The mean for a sample of difference scores
B)The mean for a population of difference scores
C)The difference between two population means
D)The difference between two sample means

Accepted Answer

A confidence interval using the repeated-measures t statistic estimates the mean for a population of difference scores, reflecting the average change in measurements taken from the same subjects under two different conditions or at two different times.

Question 4

In general,what characteristics of the difference scores are most likely to produce a significant t statistic for the repeated-measures hypothesis test?
A)A large number of scores and a large variance
B)A large number of scores and a small variance
C)A small number of scores and a large variance
D)A small number of scores and a small variance

Accepted Answer

A large number of scores helps to increase the power of the test, but a small variance in the difference scores means that there is less variability in the data and a stronger signal indicating a significant difference between the two conditions. This combination of a large sample size and small variance is most likely to produce a significant t statistic in a repeated-measures hypothesis test.

Question 5

For a repeated-measures study comparing two treatment conditions,a researcher obtains Cohen's d = 0.50 for a sample of n = 4 scores with a variance of s²= 16.What is the value of the sample mean? A)M_D = 2 B)M_D = 4 C)M_D = 8 D)M_D = 16

Accepted Answer

The answer of For a repeated-measures study comparing two treatment...

Question 6

In general,what is the effect of an increase in the variance for the sample of difference scores?
A)An increase in the standard error and an increase in the value of t
B)An increase in the standard error and a decrease in the value of t
C)A decrease in the standard error and an increase in the value of t
D)A decrease in the standard error and a decrease in the value of t

Accepted Answer

The standard error is calculated as the standard deviation of the sample of difference scores divided by the square root of the sample size. An increase in the variance of the sample of difference scores would result in a larger standard deviation, and therefore a larger standard error. This would make it more likely that any observed difference between the means of the two groups is due to chance, resulting in a decrease in the value of t.

Question 7

What is indicated by a large variance for a sample of difference scores?
A)A consistent treatment effect and a high likelihood of a significant difference
B)A consistent treatment effect and a low likelihood of a significant difference
C)An inconsistent treatment effect and a high likelihood of a significant difference
D)An inconsistent treatment effect and a low likelihood of a significant difference

Accepted Answer

A large variance for a sample of difference scores indicates an inconsistent treatment effect and a low likelihood of a significant difference. This is because the difference scores are measuring the change in a variable from one point to another, and if there is a large variance in those scores, it suggests that the change is not consistent across the sample. Therefore, there is less support for the idea that the treatment had a significant effect overall.

Question 8

A research report describing the results from a repeated-measures study states that the data show no significant difference between the two treatments,t(10)= 1.65,p > .05.Based on this report,how many individuals participated in the research study?
A)9
B)10
C)11
D)12

Accepted Answer

In a repeated-measures study, the degrees of freedom (df) for a t-test are calculated as n - 1, where n is the number of participants. Given that df = 10, we solve for n: n - 1 = 10, thus n = 11.

Question 9

A researcher reports t(12)= 2.86,p < .05 for a repeated-measures research study.How many individuals participated in the study?
A)n = 11
B)n = 13
C)n = 24
D)n = 25

Accepted Answer

The t-value and p-value indicate that the results are statistically significant at the p < .05 level. Since this is a repeated-measures study, we know that the sample size must be less than or equal to 2 times the number of levels/groups in the study. Since we only have one t-score reported, we can assume that there were only two levels/groups in the study. This means that the total number of participants in the study must be 13 (i.e. n = 13).

Question 10

A researcher obtains t = 2.25 for a repeated-measures study using a sample of n = 10 participants.Based on this t value,what is the correct decision for a two-tailed test?
A)Reject the null hypothesis with α = .05 but not 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 make a decision without additional information

Accepted Answer

The answer of A researcher obtains t = 2.25 for...

Question 11

A researcher is using a repeated-measures study to evaluate the difference between two treatments.If the difference between the treatments is consistent from one participant to another,then the data should produce ______.
A)a small variance for the difference scores and a small standard error
B)a small variance for the difference scores and a large standard error
C)a large variance for the difference scores and a small standard error
D)a large variance for the difference scores and a large standard error

Accepted Answer

A consistent difference between the treatments for each participant would result in a small variance for the difference scores (as the differences would be similar across participants) and a small standard error (as the data points would cluster tightly around the mean difference score).

Question 12

Assuming that other factors are held constant,which of the following would tend to increase the likelihood of rejecting the null hypothesis?
A)Decrease the sample size
B)Increase the sample mean difference
C)Increase the sample variance
D)None of the other 3 options would increase the likelihood.

Accepted Answer

Increasing the sample mean difference would make the observed difference between the sample means more extreme and less likely to occur by chance, making it more probable that the null hypothesis is false and should be rejected. Decreasing the sample size or increasing the sample variance would increase the chance of observing results consistent with the null hypothesis and decrease the likelihood of rejecting it.

Question 13

A researcher uses a repeated-measures design to compare individuals' performance before treatment with their performance after treatment.If all of the participants show improved performance of 8 or 9 points after treatment,what should the researcher find?
A)The sample mean difference is near zero.
B)The t statistic is near zero.
C)The variance of the difference scores is near zero.
D)None of the other options is correct.

Accepted Answer

The variance of the difference scores is near zero because all participants show similar improvement, indicating little variability in the difference scores.

Question 14

A research report describing the results from a repeated-measures t test states that "t(22)= 1.71,p > .05." From this report,what was the outcome of the hypothesis test?
A)Reject the null hypothesis with a sample of n = 23 participants
B)Fail to reject the null hypothesis with a sample of n = 23 participants
C)Reject the null hypothesis with a sample of n = 22 participants
D)Fail to reject the null hypothesis with a sample of n = 22 participants

Accepted Answer

The t-value is 1.71, which is not significant at the .05 level given the degrees of freedom of 22(n-1). Therefore, we fail to reject the null hypothesis with a sample of n= 23 participants.

Question 15

A sample of n = 9 college students is used to evaluate the effectiveness of a new Study Skills Workshop.Each student's grade point average (GPA)is recorded for the semester before the workshop and for the semester after the workshop.The average GPA improved by M_D = 0.60 points with s² = 0.09.The researcher would like to use the sample to estimate how much effect the workshop would have for the entire college population.Which of the following is the 80% confidence interval for these data? A)µ_D = 0.60 + 0.01(1.397) B)µ_D = 0.60 + 0.09(1.860) C)µ_D = 0.60 + 0.10(1.397) D)µ_D = 0.60 + 0.10(1.860)

Accepted Answer

The answer of A sample of n = 9 college...

Question 16

If other factors are held constant,which of the following sets of data is most likely to produce a significant value for the repeated-measures t statistic?
A)n = 15 and SS = 10 for the difference scores
B)n = 15 and SS = 100 for the difference scores
C)n = 30 and SS = 10 for the difference scores
D)n = 30 and SS = 100 for the difference scores

Accepted Answer

The repeated-measures t statistic is more likely to be significant with a larger sample size (n) and a smaller sum of squares (SS) for the difference scores, as this suggests less variability and more reliability in the differences measured. Therefore, option C (n = 30 and SS = 10) is most likely to produce a significant value because it combines a relatively large sample size with low variability in the difference scores.

Question 17

If other factors are held constant,which of the following sets of data is most likely to produce a significant value for the repeated-measures t statistic? A)n = 15 and M_D = 2 B)n = 15 and M_D = 4 C)n = 30 and M_D = 2 D)n = 30 and M_D = 4

Accepted Answer

The repeated-measures t statistic measures the difference between two dependent means, so a larger M_D (within-group variance) and sample size (n) will increase the likelihood of a significant result. Therefore, D (n = 30, M_D = 4) is the set of data most likely to produce a significant value for the repeated-measures t statistic.

Question 18

Which of the following describes the effect of an increase in the variance of the difference scores?
A)Measures of effect size and the likelihood of rejecting the null hypothesis both decrease.
B)Measure of effect size increase,but the likelihood of rejecting the null hypothesis decreases.
C)There is little or no effect on measures of effect size,but the likelihood of rejecting the null hypothesis increases.
D)There is little or no effect on measures of effect size,but the likelihood of rejecting the null hypothesis decreases.

Accepted Answer

An increase in the variance of the difference scores leads to a decrease in the effect size and reduces the likelihood of rejecting the null hypothesis due to increased variability.

Question 19

Which of the following describes the effect of increasing sample size?
A)Measures of effect size and the likelihood of rejecting the null hypothesis both increase.
B)Measure of effect size increase,but the likelihood of rejecting the null hypothesis decreases.
C)There is little or no effect on measures of effect size,but the likelihood of rejecting the null hypothesis increases.
D)There is little or no effect on measures of effect size,but the likelihood of rejecting the null hypothesis decreases.

Accepted Answer

Increasing sample size generally increases the power of a statistical test, making it more likely to reject the null hypothesis if it is false, but it does not affect the effect size.

Question 20

A researcher obtains t(20)= 2.00 and M_D = 9 for a repeated-measures study.If the researcher measures effect size using the percentage of variance accounted for,what value will be obtained for r²? A)9/20 B)9/29 C)4/13 D)4/24

Accepted Answer

The answer of A researcher obtains t(20)= 2.00 and M_D...

Quiz 11: The T Test for Two Related Samples

In general,if the variance of the difference scores increases,what will happen to the value of the t statistic?

What value is estimated with a confidence interval using the repeated-measures t statistic?

In general,what characteristics of the difference scores are most likely to produce a significant t statistic for the repeated-measures hypothesis test?

For a repeated-measures study comparing two treatment conditions,a researcher obtains Cohen's d = 0.50 for a sample of n = 4 scores with a variance of s²= 16.What is the value of the sample mean?

In general,what is the effect of an increase in the variance for the sample of difference scores?

What is indicated by a large variance for a sample of difference scores?

A research report describing the results from a repeated-measures study states that the data show no significant difference between the two treatments,t(10) = 1.65,p > .05.Based on this report,how many individuals participated in the research study?

A researcher reports t(12) = 2.86,p < .05 for a repeated-measures research study.How many individuals participated in the study?

A researcher obtains t = 2.25 for a repeated-measures study using a sample of n = 10 participants.Based on this t value,what is the correct decision for a two-tailed test?

A researcher is using a repeated-measures study to evaluate the difference between two treatments.If the difference between the treatments is consistent from one participant to another,then the data should produce ______.

Assuming that other factors are held constant,which of the following would tend to increase the likelihood of rejecting the null hypothesis?

A researcher uses a repeated-measures design to compare individuals' performance before treatment with their performance after treatment.If all of the participants show improved performance of 8 or 9 points after treatment,what should the researcher find?

A research report describing the results from a repeated-measures t test states that "t(22) = 1.71,p > .05." From this report,what was the outcome of the hypothesis test?

If other factors are held constant,which of the following sets of data is most likely to produce a significant value for the repeated-measures t statistic?

If other factors are held constant,which of the following sets of data is most likely to produce a significant value for the repeated-measures t statistic?

Which of the following describes the effect of an increase in the variance of the difference scores?

Which of the following describes the effect of increasing sample size?

A researcher obtains t(20) = 2.00 and M_D = 9 for a repeated-measures study.If the researcher measures effect size using the percentage of variance accounted for,what value will be obtained for r²?

Quiz 11: The T Test for Two Related Samples

In general,if the variance of the difference scores increases,what will happen to the value of the t statistic?

What value is estimated with a confidence interval using the repeated-measures t statistic?

In general,what characteristics of the difference scores are most likely to produce a significant t statistic for the repeated-measures hypothesis test?

For a repeated-measures study comparing two treatment conditions,a researcher obtains Cohen's d = 0.50 for a sample of n = 4 scores with a variance of s2 = 16.What is the value of the sample mean?

In general,what is the effect of an increase in the variance for the sample of difference scores?

What is indicated by a large variance for a sample of difference scores?

A research report describing the results from a repeated-measures study states that the data show no significant difference between the two treatments,t(10) = 1.65,p > .05.Based on this report,how many individuals participated in the research study?

A researcher reports t(12) = 2.86,p < .05 for a repeated-measures research study.How many individuals participated in the study?

A researcher obtains t = 2.25 for a repeated-measures study using a sample of n = 10 participants.Based on this t value,what is the correct decision for a two-tailed test?

A researcher is using a repeated-measures study to evaluate the difference between two treatments.If the difference between the treatments is consistent from one participant to another,then the data should produce ______.

Assuming that other factors are held constant,which of the following would tend to increase the likelihood of rejecting the null hypothesis?

A researcher uses a repeated-measures design to compare individuals' performance before treatment with their performance after treatment.If all of the participants show improved performance of 8 or 9 points after treatment,what should the researcher find?

A research report describing the results from a repeated-measures t test states that "t(22) = 1.71,p > .05." From this report,what was the outcome of the hypothesis test?

If other factors are held constant,which of the following sets of data is most likely to produce a significant value for the repeated-measures t statistic?

If other factors are held constant,which of the following sets of data is most likely to produce a significant value for the repeated-measures t statistic?

Which of the following describes the effect of an increase in the variance of the difference scores?

Which of the following describes the effect of increasing sample size?

A researcher obtains t(20) = 2.00 and MD = 9 for a repeated-measures study.If the researcher measures effect size using the percentage of variance accounted for,what value will be obtained for r2?

For a repeated-measures study comparing two treatment conditions,a researcher obtains Cohen's d = 0.50 for a sample of n = 4 scores with a variance of s²= 16.What is the value of the sample mean?

A researcher obtains t(20) = 2.00 and M_D = 9 for a repeated-measures study.If the researcher measures effect size using the percentage of variance accounted for,what value will be obtained for r²?