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 S Red 15 7.2 0.6 White 12 6.1 0.4 Table 1 Does red increase men's attraction to women? To determine the possible effect size of the red background over the white, find a 95% confidence interval for the difference in mean attractiveness rating Mr - Mw, where 4 r represents the mean rating with the red background and Mw represents the mean rating with the white background. Round your answers to two decimal places. The 95% confidence interval is to i 1Data approximated from information given in Elliot A. and Niesta, D., "Romantic Red: Red Enhances Men's Attraction to Women," Journal of Personality and Social Psychology, 2008; 95(5): 1150-1164. Save for Later Attempts: 0 of 4 used Submit Answer

Answer 1

The 95% confidense interval is given by:

(X̄1- X̄2)  ± t * S.E(X̄1- X̄2)

Where X̄1 is mean of first group , X̄2 is mean of second group, t is obtained from student's t table with significance level 0.05 and degrees of freedom n1+n2-2 and S.E(X̄1- X̄2) is standard error of (X̄1- X̄2)

Here, X̄1 = 7.2

X̄2 = 6.1

n1=15

n2=12

S.E(X̄1- X̄2) = sqrt [ ((s²_p/n₁) + (s²_p/n₂)) ]

where s²_p  is the pooled variance given by

((n1-1)(s²₁) + (n2-1)(s²₂)) / (n1+n2-2)

Given S1=0.6 and S2=0.4

On calculation, s²_p = 0.272

S.E(X̄1- X̄2) = 0.2

From students t table, t = 2.06

Therefore, the 95% confidence interval for difference in mean rating is given by:

(7.2-6.1) ± (2.06 * 0.2)

= 1.1  ± 0.412

= [ 0.69 , 1.51 ]

The 95% confidense interval is 0.69 to 1.51