Question

Does Red Increase Men’s Attraction to Women?

A study examines 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). Men in one group were shown pictures of women on a white background while the men in the other group were shown the same pictures of women on a red background. The results are shown in Table 1 and the data for both groups are reasonably symmetric with no outliers.

Color n X-bar s

Red 15 7.2 . 0.6

White 12 . 6.1 . 0.4

To determine the possible effect size of the red background over the white, find a 90% confidence interval for the difference in mean attractiveness rating , where represents the mean rating with the red background and represents the mean rating with the white background. Round your answers to two decimal places. The 90% confidence interval is

Answer 1

solution:-
given that
x1 = 7.2 x2 = 6.1
s1 = 0.6 s2 = 0.4
n1 = 15 n2 = 12

formula for confidence interval

(x1 - x2) +/- t * sqrt(s1^2/n1 + s2^2/n2)

degrees of freedom = (n1+n2)-2 = (15+12)-2 = 25

90% confidence with degrees of freedom is t = 1.708

=> (7.2-6.1) +/- 1.708 * sqrt((0.6^2/15) + (0.4^2/12))

=> 1.1 +/- 0.33

=> (0.77 , 1.43)