A theater arts department enlisted the help of a social psychology professor to design a study to see if being surrounded by highly attractive people affected the performance of young actors. Thirty student actors were randomly assigned to act a particular scene under one of two conditions: For 13 of the actors, the other performers were dressed and made up to look very attractive; for the other 17 actors, the other performers were dressed and made up to look very unattractive. A panel of judges rated the performance of the two groups, and the mean performance ratings for the actors with attractive co-performers was 4.3 (S = .86) and with unattractive co-performers, the mean was 5.4 (S = 1.30). Using the .05 significance level, did acting with attractive co-performers affect performance?
a. Use the five steps of hypothesis testing.
b. Sketch the distributions involved.
c. Figure the effect size.
d. Explain the logic of what you did to a person who is familiar with the t test for a single sample, but who is unfamiliar with the t test for independent means. Be sure you explain how this problem differs from a t test for a single sample. Your answer should consist mainly of a thorough explanation of the characteristics of the comparison distribution and the logic of all the steps of figuring you did to determine those characteristics.