Question 1

Which of the following is an example of two dependent samples?

Accepted Answer

The pretest and posttest scores of the same group of children are dependent because they involve the same subjects measured at two different times.

Question 2

Which of the following is an example of two dependent samples?

Accepted Answer

Dependent samples are those where the observations in one sample can be paired with observations in the other sample. In option D, the weight of individuals before and after starting a weight loss program involves the same individuals, making these samples dependent.

Question 3

Which one of the following procedures is recommended when the distribution is platikurtic?

Accepted Answer

O'Brien's test is recommended for platykurtic distributions as it is designed to be more robust to deviations from normality, including differences in kurtosis.

Question 4

Which one of the following procedures is recommended when the distribution is mesokurtic?

Accepted Answer

O'Brien's test is recommended for mesokurtic distributions, which are distributions with kurtosis similar to that of a normal distribution. This test is designed to be more robust for data that does not deviate significantly in kurtosis from normality.

Question 5

Which one of the following procedures is recommended when the distribution is leptokurtic?

Accepted Answer

O'Brien's test is recommended for distributions that are leptokurtic because it is designed to be more robust to deviations from normality, including issues with kurtosis.

Question 6

A researcher computes the O'Brien procedure and finds an F test statistic of 2.22 and an F critical value of 2.01. Which of the following can be determined?

Accepted Answer

The F test statistic is less than the F critical value, indicating that the variances of the groups are not statistically different.

Question 7

A researcher computes the O'Brien procedure and finds an F test statistic of 3.81 and an F critical value of 2.61. Which of the following can be determined?

Accepted Answer

Since the F test statistic (3.81) is greater than the F critical value (2.61), it indicates that the variances of the groups are statistically different, leading to the rejection of the null hypothesis that suggests no difference in variances.

Question 8

A researcher computes the Brown-Forsythe procedure and finds an F test statistic of 4.75 and an F critical value of 3.32. Which of the following can be determined?

Accepted Answer

Since the F test statistic (4.75) is greater than the F critical value (3.32), it indicates that the variances of the groups are statistically different at the chosen significance level.

Question 9

A researcher computes the Brown-Forsythe procedure and finds an F test statistic of 2.35 and an F critical value of 3.78. Which of the following can be determined?

Accepted Answer

Since the F test statistic (2.35) is less than the F critical value (3.78), we fail to reject the null hypothesis, indicating that there is not enough evidence to say the variances are statistically different.

Question 10

A researcher conducted the Brown-Forsythe procedure and reports an alpha level of .05 and p value of .80. Which of the following is a correct statement based on this information?

Accepted Answer

The p value of .80 is much higher than the alpha level of .05, indicating that the differences in variances are not statistically significant.

Question 11

A researcher conducted the Brown-Forsythe procedure and reports an alpha level of .01 and p value of .005. Which of the following is a correct statement based on this information?

Accepted Answer

The p value (.005) is less than the alpha level (.01), indicating that the difference in variances is statistically significant.

Question 12

A researcher conducted the Brown-Forsythe procedure and reports an alpha level of .01 and p value of .10. Which of the following is a correct statement based on this information?

Accepted Answer

The p value (.10) is greater than the alpha level (.01), indicating that the difference in variances is not statistically significant.

Question 13

A researcher conducted the O'Brien procedure and reports an alpha level of .10 and p value of .05. Which of the following is a correct statement based on this information?

Accepted Answer

The O'Brien procedure is used to test for homogeneity of variances among groups. Since the p-value (.05) is less than the alpha level (.10), we reject the null hypothesis, indicating that the variances of the groups are statistically different.

Question 14

A researcher conducted the O'Brien procedure and reports an alpha level of .05 and p value of .20. Which of the following is a correct statement based on this information?

Accepted Answer

The p value of .20 is greater than the alpha level of .05, indicating that the differences in variances are not statistically significant.

Question 15

A researcher wants to determine if the sample variance for the number of hours spent studying per week for a sample of college students is different than 15. Which one of the following procedures is appropriate to test this?

Accepted Answer

The appropriate procedure to test if the sample variance for the number of hours spent studying per week for a sample of college students is different than a specific value (in this case, 15) is to perform a test for a single variance. This test compares the observed sample variance to a specified value to determine if there is a significant difference.

Question 16

A researcher samples high school seniors and wants to determine if the variance of college entrance exam scores for the seniors prior to completing a test taking course is lower than the variance of college entrance exam scores for the same group of seniors after completing a test taking course. Which one of the following procedures is appropriate to test this?

Accepted Answer

The appropriate procedure is to test for two dependent variances because the same group of seniors is being measured before and after completing a test taking course, making the two sets of scores dependent on each other.

Question 17

A researcher samples cheerleaders and wants to determine if the variance of the number of cartwheels conducted during a football game prior to attending cheer camp is different than the variance of the number of cartwheels conducted during a football game after attending cheer camp. Which one of the following procedures is appropriate to test this?

Accepted Answer

The researcher is comparing the variance of the number of cartwheels conducted during a football game prior to attending cheer camp to the variance of the number of cartwheels conducted during a football game after attending cheer camp. This is a test for two dependent variances.

Question 18

A researcher samples parents of charter school transfer students and wants to determine if the variance of their child's satisfaction with school prior to transferring to the charter school is lower than the variance of their child's satisfaction with school after transferring to the charter school. Which one of the following procedures is appropriate to test this?

Accepted Answer

The researcher wants to compare the variance of satisfaction before and after transferring to the charter school, which is a test for two dependent variances.

Question 19

A researcher samples unemployed workers and wants to determine if the variance of depression scores for the unemployed prior to becoming unemployed is higher than the variance of depression scores for the unemployed after becoming unemployed. Which one of the following procedures is appropriate to test this?

Accepted Answer

The researcher is comparing the variance of depression scores for the same group of individuals before and after becoming unemployed, which makes the samples dependent. Therefore, a test for two dependent variances is appropriate.

Question 20

A researcher wants to determine if the variance of points scored by teams who have won a national championship differs from the variance of points scored by teams who have not won a national championship. Which one of the following procedures is appropriate to test this?

Accepted Answer

The appropriate procedure is a test for two independent variances because the teams are divided into two independent groups: those who have won a national championship and those who have not. The goal is to compare the variance in points scored between these two distinct groups.

Quiz 9: Inferences About Variances

Which of the following is an example of two dependent samples?

Which of the following is an example of two dependent samples?

Which one of the following procedures is recommended when the distribution is platikurtic?

Which one of the following procedures is recommended when the distribution is mesokurtic?

Which one of the following procedures is recommended when the distribution is leptokurtic?

A researcher computes the O'Brien procedure and finds an F test statistic of 2.22 and an F critical value of 2.01. Which of the following can be determined?

A researcher computes the O'Brien procedure and finds an F test statistic of 3.81 and an F critical value of 2.61. Which of the following can be determined?

A researcher computes the Brown-Forsythe procedure and finds an F test statistic of 4.75 and an F critical value of 3.32. Which of the following can be determined?

A researcher computes the Brown-Forsythe procedure and finds an F test statistic of 2.35 and an F critical value of 3.78. Which of the following can be determined?

A researcher conducted the Brown-Forsythe procedure and reports an alpha level of .05 and p value of .80. Which of the following is a correct statement based on this information?

A researcher conducted the Brown-Forsythe procedure and reports an alpha level of .01 and p value of .005. Which of the following is a correct statement based on this information?

A researcher conducted the Brown-Forsythe procedure and reports an alpha level of .01 and p value of .10. Which of the following is a correct statement based on this information?

A researcher conducted the O'Brien procedure and reports an alpha level of .10 and p value of .05. Which of the following is a correct statement based on this information?

A researcher conducted the O'Brien procedure and reports an alpha level of .05 and p value of .20. Which of the following is a correct statement based on this information?

A researcher wants to determine if the sample variance for the number of hours spent studying per week for a sample of college students is different than 15. Which one of the following procedures is appropriate to test this?

A researcher wants to determine if the variance of points scored by teams who have won a national championship differs from the variance of points scored by teams who have not won a national championship. Which one of the following procedures is appropriate to test this?