Question 1

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

Accepted Answer

Large sample sizes increase the precision of the estimate of the population mean, and small sample variances reduce the standard error of the mean. Together, these conditions increase the likelihood of finding a statistically significant difference between the two sample means when using the independent-measures t statistic.

Question 2

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.

Accepted Answer

This is an example of a repeated-measures design where the same group of participants' weights are measured before and after the diet. In an independent-measures design, two separate groups of participants would be used (e.g., one group on the diet and one group not on the diet).

Question 3

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.

Accepted Answer

The estimated standard error in an independent-measures t statistic quantifies the expected variability between the sample means if the samples are drawn from the same population, essentially measuring how much difference is considered normal due to sampling error.

Question 4

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.

Accepted Answer

The pooled variance is calculated by taking a weighted average of the two sample variances, where the weights are based on the sample sizes. Therefore, the pooled variance will always be between the two sample variances. In this case, since 12 is smaller than 15, the pooled variance must fall between these two values. Therefore, the statement is true.

Question 5

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.

Accepted Answer

The homogeneity of variance assumption assumes that the two populations under consideration have equal variances. This is important when carrying out hypothesis tests or constructing confidence intervals for the difference between two population means using two independent samples. The assumption allows for the use of a pooled variance estimate, which improves the accuracy of the test or interval construction. Option A is incorrect because it assumes equal variances within the samples, not the populations. Option B is incorrect because it contradicts the assumption. Option D is incorrect because it is not a relevant assumption for this situation.

Question 6

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

Accepted Answer

A large mean difference between the two groups indicates a significant difference in the independent variable being studied. Small sample variances reduce the spread of data points and increase the likelihood of a significant t-value. A large effect size indicates a strong relationship between the independent and dependent variables. Therefore, option B is most likely to produce a significant t-value and a large effect size.

Question 7

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.

Accepted Answer

The homogeneity of variance assumption is concerned with the equality of variances, not the mean differences. All options have relatively similar variances, so they are equally likely to satisfy the assumption.

Question 8

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.

Accepted Answer

The answer of If other factors are held constant,which of...

Question 9

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

Accepted Answer

This is true, as the pooled variance is needed to estimate the standard error in the independent-measures t statistic formula.

Question 10

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.

Accepted Answer

The pooled variance is calculated by dividing the sum of the two sum of squares (SS1 + SS2) by the total number of scores from both samples minus the number of samples (n1 + n2 - 2), not the total number of scores (n1 + n2). So, it should be (40 + 20) / (5 + 5 - 2) = 60 / 8 = 7.5.

Question 11

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

Accepted Answer

An independent-measures study with n = 20 scores in each treatment will have degrees of freedom (df) calculated as df = (n1 - 1) + (n2 - 1), where n1 and n2 are the sample sizes of the two groups. Therefore, for n = 20 in each group, df = (20 - 1) + (20 - 1) = 38.

Question 12

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

Accepted Answer

When the two samples are the same size, the pooled variance will equal the weighted average of the two sample variances (weighted by the sample size minus 1), which is equivalent to the average of the two sample variances. Therefore, the statement is true.

Question 13

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

Accepted Answer

When the two samples are the same size, the degrees of freedom for the independent measures t statistic will be (n1 + n2) - 2, which is an even number. For example, if both samples have 10 observations, the degrees of freedom would be (10 + 10) - 2 = 18, which is even. Therefore, the statement is true.

Question 14

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

Accepted Answer

Increasing the sample size increases the power of the test, which means that the likelihood of rejecting the null hypothesis increases. However, increasing sample size does not have a significant effect on the measure of effect size (such as Cohen's d), which reflect the practical significance of the difference between the means. Therefore, option C correctly describes the effect of increasing sample size on these parameters.

Question 15

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.

Accepted Answer

The formula for pooled variance is (SS1 + SS2) / (n1 + n2 - 2).
Using the given values, we get (40 + 80) / (7 + 5 - 2) = 120/10 = 12. Therefore, the statement is true.

Question 16

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

Accepted Answer

Larger sample sizes and larger mean differences both contribute to finding statistically significant results. Option D combines a relatively large sample size (n = 10 for both samples) with a relatively large mean difference (10 points), making it the most likely to produce a significant mean difference.

Question 17

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

Accepted Answer

Cohen's d is calculated as the difference between two means divided by the pooled standard deviation. The larger the mean difference and the smaller the pooled variance, the larger the Cohen's d value. Option B has the largest mean difference with a moderate pooled variance, leading to the largest Cohen's d value.

Question 18

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.

Accepted Answer

The independent-measures t statistic is larger when the difference between the sample means is larger and the variances are smaller. Option C has the largest difference between means (10) with relatively smaller variances compared to option D, making it the choice that would produce the largest t statistic.

Question 19

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

Accepted Answer

This is the correct formula for determining the degrees of freedom for an independent-measures t test when both samples have the same number of scores, so the statement is true.

Question 20

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

Accepted Answer

Large sample size reduces random variability, making it more likely to detect a significant difference. A smaller variance also increases the likelihood of detecting a significant difference, as the means of the two groups will be more distinct from each other.

Quiz 10: The t Test for Two Independent Samples

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 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.

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.

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.

What is assumed by the homogeneity of variance assumption?

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

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

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

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

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.

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

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

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

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

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.

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

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

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

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

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