In a study similar to one conducted by Fallon and Rozin (1985). a psychologist prepared a set of silhouettes showing different female body shapes ranging from somewhat thin to somewhat heavy and asked a group of women to indicate which body figure they thought men would consider the most attractive. Then a group of men were shown the same set of profiles and asked which image they considered the most attractive. The following hypothetical data show the number of individuals who selected each of the four body image profiles.
a. Do the data indicate a significant difference between the actual preferences for the men and the preferences predicted by the women? Test at the .05 level of significance.
b. Compute the phi-coefficient to measure the strength of the relationship.
|Body Image Profiles|
|Somewhat Thin||Slightly Thin||Slightly Heavy||Somewhat Heavy|
To Find: If there is a significant difference between the actual preferences for the men and the preferences predicted by the women.
A sample of 140 participants were involved in a study. The distribution is given in the question. Use to test the claim.
|Somewhat thin||Slightly thin||Slightly heavy||Somewhat heavy||total|
Step 1: Null Hypothesis and Alternate Hypothesis are:
There is no significant relationship between the actual preferences for the men and women
Significant relationship between actual preferences for the men and women
Step 2: For the given sample, degrees of freedom equals:
With and , the critical value (CV) is obtained from the as
Step 3: is calculated as:
The formula to calculate expected frequency is:
Substitute in the above formula and compute respective values of expected frequencies:
For the row 1, the expected frequencies are:
To Find: The value of phi-coefficient for the given question.
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