Color affects us in many ways. For example, Exercise C.51 on page 452 describes an experiment showing that the color red appears to enhance men’s attraction to women. Previous studies have also shown that athletes competing against an opponent wearing red perform worse, and students exposed to red before a test perform worse. A recent study states that ‘‘red is hypothesized to impair performance on achievement tasks, because red is associated with the danger of failure.” In the study, US college students were asked to solve 15 moderately difficult, five-letter, single-solution anagrams during a 5-minute period. Information about the study was given to participants in either red, green, or black ink just before they were given the anagrams. Participants were randomly assigned to a color group and did not know the purpose of the experiment, and all those coming in contact with the participants were blind to color group. The red group contained 19 participants and they correctly solved an average of 4.4 anagrams. The 27 participants in the green group correctly solved an average of 5.7 anagrams and the 25 participants in the black group correctly solved an average of 5.9 anagrams. Work through the details below to test if performance is different based on prior exposure to different colors.

(a) State the hypotheses.

(b) Use the fact that sum of squares for color groups is 27.7 and the total sum of squares is 84.7 to complete an ANOVA table and find the Fstatistic.

(c) Use the F-distribution to find the p-value. 

(d) Clearly state the conclusion of the test.

Data from C.51

A recent study examined the impact of the color red on how attractive men perceive women to be. In the study, men were randomly divided into two groups and were asked to rate the attractiveness of women on a scale of 1 (not at all attractive) to 9 (extremely attractive). One group of men were shown pictures of women on a white background and the other group were shown the same pictures of women on a red background. The men who saw women on the red background rated them as more attractive. All participants and those showing the pictures and collecting the data were not aware of the purpose of the study.