Question 1

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 being compared have equal variances. It does not assume that the two samples have equal variances or that the two population variances are not equal.

Question 2

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 true. When both samples have the same number of scores (n), the formula for the degrees of freedom in the independent-measures t-test is df = n1 + n2 - 2, which can be simplified to df = 2n - 2 when both samples have the same size (n1 = n2 = n).

Question 3

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

Accepted Answer

Large sample sizes and small sample variances increase the likelihood of obtaining a significant t statistic because they reduce the standard error, making it easier to detect a true difference between the sample means.

Question 4

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 number of scores in the samples will increase the precision of the estimate of the means, which will increase the power of the test and, thus, increase the likelihood of rejecting the null hypothesis. However, it will have little or no effect on measures of effect size because effect size is a standardized measure that expresses the difference between the means in standard deviation units.

Question 5

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

When the samples are large, it increases the chances of finding significant differences. When the variance is small, it means that the data points are closer to the mean, which increases the chances of obtaining a significant value for an independent-measures t statistic.

Question 6

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

Accepted Answer

The formula for the estimated standard error in an independent-measures t-test includes the pooled variance as one of the components. Therefore, the pooled variance must be calculated before the estimated standard error can be calculated.

Question 7

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.

Accepted Answer

The largest value of the independent-measures t statistic would come from the data with the largest difference between the sample means and the smallest variability within each group. Option C has the largest difference between sample means (10 and 20), and the smallest variability within each group (variances of 20 and 25).

Question 8

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 9

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

This statement is true as the pooled variance is calculated by combining the variances from each sample and weighting them based on their sample size. Since the second sample has a larger value for s², it is likely to have a larger variance, therefore the pooled variance would fall between 12 and 15.

Question 10

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 because the same participants' weights are being measured before and after the diet, and the two measurements are being compared. In an independent-measures design, different groups of participants would be measured before and after the intervention.

Question 11

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 squared deviations for both samples by the degrees of freedom, which is n1 + n2 - 2. The correct calculation for pooled variance in this case is (40+20)/(5+5-2) = 6. However, the question incorrectly states that the pooled variance is 60/10.

Question 12

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 13

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

Accepted Answer

When the two samples are the same size, the degrees of freedom for the independent measures t statistic will be even. The formula for degrees of freedom is (n1 + n2) - 2, where n1 and n2 are the sample sizes. If the two samples are the same size, then the formula becomes 2*n - 2, which is an even number.

Question 14

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 15

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

Question 16

Which set of sample characteristics is most likely to produce a significant value for the independent-measures t statistic and a large measure of 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 indicates a greater difference between the two groups being compared, which can increase the likelihood of a significant t statistic. Additionally, small sample variances will decrease the standard error of the mean difference, making it easier to detect meaningful differences. A large effect size would also be more likely with a large mean difference.

Question 17

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), which in this case is (40 + 80)/(7 + 5 - 2) = 120/10 = 12. Therefore, the statement is true.

Question 18

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 19

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

Accepted Answer

This is true. The formula for pooled variance is (s1^2 + s2^2) / 2, where s1^2 and s2^2 are the variances of the two samples. If the two samples are the same size, then the denominator is 2, and the formula simplifies to (s1^2 + s2^2) / 2 = (2s^2) / 2 = s^2, where s^2 is the average of the two sample variances.

Question 20

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.

Quiz 10: The T Test for Two Independent Samples

What is assumed by the homogeneity of variance assumption?

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

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?

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

Which combination of factors is most likely to produce a significant 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.

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

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.

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.

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,the independent measures t statistic will have an even number for degrees of freedom.

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

If other factors are held constant,which of the following sets of data is most likely to satisfy 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 measure of effect size?

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 would produce the largest value for an independent-measures t statistic?

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

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

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.