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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

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
 
Women 29 25 IK 8 80
Men 11 15 22 12 60
  40 40 40 20  

a.

To determine

To Find: If there is a significant difference between the actual preferences for the men and the preferences predicted by the women.

Explanation

Given info:

A sample of 140 participants were involved in a study. The distribution is given in the question. Use α=0.05 to test the claim.

  Somewhat thin Slightly thin Slightly heavy Somewhat heavy total
Women 29 25 18 8 80
men 11 15 22 12 60
Total 40 40 40 20 140

Calculations:

Step 1: Null Hypothesis and Alternate Hypothesis are:

H0: There is no significant relationship between the actual preferences for the men and women

H1: Significant relationship between actual preferences for the men and women

Step 2: For the given sample, degrees of freedom equals:

df=(R1)(C1)   where R equals number of rows and C equals columns=(21)(41)=3

With α=0.05 and df=3, the critical value (CV)  is obtained from the χ2table as

χ2=7.815

Step 3: χ2statistics is calculated as:

χ2=(fofe)2fe

The formula to calculate expected frequency is:

fe=fcfrn...where fr is row frequency and fc is column frequency

Substitute n=140 in the above formula and compute respective values of expected frequencies:

For the row 1, the expected frequencies are:

fe,f_some_thin=40×80140fe,f_slight_thin=40×80140fe,f_slight_heavy=40</

b.

To determine

To Find: The value of phi-coefficient for the given question.

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