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Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570

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BuyFindarrow_forward

Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570
Textbook Problem

Research indicates that the color red increases men's attraction to women (Elliot & Niesta, 2008). In the original study, men were shown women's photographs presented on either a white or a red background. Photographs presented on red were rated significantly more attractive than the same photographs mounted on white. In a similar study, a researcher prepares a set of 30 women's photographs, with 15 mounted on a white background and 15 mounted on red. One picture is identified as the test photograph and appears twice in the set. Once on white and once on red. Each male participant looks through the entire set of photographs and rates the attractiveness of each woman on a 10-point scale. The following table summarizes the ratings of the test photograph for a sample of n = 9 men. Are the ratings for the test photograph significantly different when it is presented on a red background compared to a white background? Use a two tailed test with α = .01.

images

To determine
Whether the ratings for the test photographs has significant difference for white background and red background.

Explanation

Given info:

The given data are shown below,

Participants White background Red background
A 4 7
B 6 7
C 5 8
D 5 9
E 6 9
F 4 7
G 3 9
H 8 9
I 6 9

Calculation:

The difference D, D and D2 is obtained below:

Participants White background Red background D D2
A 4 7 3 9
B 6 7 1 1
C 5 8 3 9
D 5 9 4 16
E 6 9 3 9
F 4 7 3 9
G 3 9 6 36
H 8 9 1 1
I 6 9 3 9
Total     28 99

Thus, the value of D is 28 and D2 is 99.

The mean difference MD:

MD=DN (1)

MD=289=3.11

Thus, the value of mean difference is 3.11.

The value of SS is,

SS=D2(D)2N (2)

SS=997849=9987

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