Investigators wish to determine if faking a strong gender identification can lead to biased results of the California Psychological Inventory. A total of 16 men and 16 women were available for the study. Two levels of treatment were considered: h) honest answers, r) role playing. Under role playing, men were asked to respond in a very "femenine" manner, while women were asked to respond in a very "macho" manner. A randomized complete block design was used. Half the men and half of the women were assigned to the honest treatment, while the other halves were assigned to the role-playing treatment. The Sp score on the test was then measured for each subject. Three hypotheses are to be considered: 1) There is no difference in Sp scores between men and women, 2) There is no difference in Sp scores between people asked to give honest answers, and those asked to role play, and 3) There is no interaction between the gender and treatments. a. Use SAS to perform a two-way analysis of variance. Attach a copy of your output to the end of this assignment. b. Test the null hypothesis that there is no gender by treatment interaction. i. Give the results of your test, test statistic, d.f., and p-value. ii. Compute the standard error of a gender by treatment mean by hand. c. Test the null hypothesis that gender has no impact on Sp scores. i. Give the results of your test, test statistic, d.f., and p-value. ii. Compute the standard error of a gender mean by hand. iii. Compute a 95% confidence interval for the mean Sp score of women. d. Test the null hypothesis that treatment has no impact on Sp scores. i. Give the results of your test, test statistic, d.f., and p-value. ii. Compute the standard error of a treatment mean by hand. iii. Compute a 95% confidence interval for the mean Sp score of role players. e. What may you conclude from the above analyses? Be thorough and make sure you provide the appropriate evidence backing up your conclusions.