Social Statistics Exam 4

1. A psychologist is interested in evaluating the effectiveness of the following three techniques for treating minor depression: cognitive restructuring, assertiveness training, and an exercise/nutrition program. Forty undergraduate students suffering from mild depression are randomly sampled from the university counseling center and randomly assigned ten each to the three techniques previously mentioned, and the remaining ten to a placebo control group. Treatment is conducted for 10 weeks and the post-treatment depression scores measured by the Beck Depression Inventory are given below. Higher scores indicate greater depression. Test the null hypothesis that there is no significant difference in depression scores by different types of treatment. Set α=.05 level.
   

2. Assume you are a nutritionist who has been asked to determine whether there is a difference in sugar content among the three leading brands of breakfast cereal (brands A, B, and C). To assess the amount of sugar in the cereals, you randomly sample six packages of each brand and chemically determine their sugar content. Descriptive statistics for the grams of sugar by each type of cereal are presented below. You may enter the data into SPSS and conduct the One-Way ANOVA analysis to help you answer the question.

3. A psychologist is interested in evaluating the effectiveness of the following three techniques for treating minor depression: cognitive restructuring, assertiveness training, and an exercise/nutrition program. Forty undergraduate students suffering from mild depression are randomly sampled from the university counseling center and randomly assigned ten each to the three techniques previously mentioned, and the remaining ten to a placebo control group. Treatment is conducted for 10 weeks and the post-treatment depression scores measured by the Beck Depression Inventory are given below. Higher scores indicate greater depression. Test the null hypothesis that there is no significant difference in depression scores by different types of treatment. Set α=.05 level.

4. A random sample of four interviewers associated with a large public opinion firm have completed four interviews each, and the time in minutes necessary to complete the interviews is indicated in the accompanying table. Results generated by SPSS are also presented below.

5. What is the proportion of the variance of the dependent variable that can be explained by the independent variable in question 4 above?.

6. What is the null hypothesis of question 4 above?

7. Which one of the following pairs shows a statistically significant difference in the time necessary to complete the interviews? (Set alpha =.05 level) reference question 4

8. What is the F value in the ANOVA table of question 4?

9. What is the value for the sum of squares between groups (SSb) in question 4?

10. Can you conclude that there is a significant difference in the time necessary to complete the interviews by four interviewers?  (Set alpha=.05 level)

11. Assume you are a nutritionist who has been asked to determine whether there is a difference in sugar content among the three leading brands of breakfast cereal (brands A, B, and C). To assess the amount of sugar in the cereals, you randomly sample six packages of each brand and chemically determine their sugar content. Descriptive statistics for the grams of sugar by each type of cereal are presented below. You may enter the data into SPSS and conduct the One-Way ANOVA analysis to help you answer the question.

___Breakfast Cereal_____

 A           B______C____

     1         7           5

     4        5           4

     3         3           4

     3         6           5

     2         4           7            

     5         7           8

 You may enter the data into SPSS and conduct the One-Way ANOVA analysis to help you answer the question.

If there is a significant difference, which pair of breakfast cereal types is not significant?

12. A psychologist is interested in evaluating the effectiveness of the following three techniques for treating minor depression: cognitive restructuring, assertiveness training, and an exercise/nutrition program. Forty undergraduate students suffering from mild depression are randomly sampled from the university counseling center and randomly assigned ten each to the three techniques previously mentioned, and the remaining ten to a placebo control group. Treatment is conducted for 10 weeks and the post-treatment depression scores measured by the Beck Depression Inventory are given below. Higher scores indicate greater depression. Test the null hypothesis that there is no significant difference in depression scores by different types of treatment. Set α=.05 level.

13. What is the F-test statistic for this test in question 12?

14. What is the alternative hypothesis of question 12?

15. What is the critical value for the test in question 12?

16. Which of the following statements is NOT an assumption for the test in question 12

I7. Is there a significant difference in depression scores by different types of treatment in question 12? Set α=.05 level.

18. If there is a significant difference in population means, use the Scheffe test to show which of the following pairs is equal in question 12.

19. Assume you are a nutritionist who has been asked to determine whether there is a difference in sugar content among the three leading brands of breakfast cereal (brands A, B, and C). To assess the amount of sugar in the cereals, you randomly sample six packages of each brand and chemically determine their sugar content. Descriptive statistics for the grams of sugar by each type of cereal are presented below. You may enter the data into SPSS and conduct the One-Way ANOVA analysis to help you answer the question.

20. Assume you are a nutritionist who has been asked to determine whether there is a difference in sugar content among the three leading brands of breakfast cereal (brands A, B, and C). To assess the amount of sugar in the cereals, you randomly sample six packages of each brand and chemically determine their sugar content. Descriptive statistics for the grams of sugar by each type of cereal are presented below. You may enter the data into SPSS and conduct the One-Way ANOVA analysis to help you answer the question.