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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

Do you view a chocolate bar as delicious or as fattening? Your attitude may depend on your gender. In a study of American college students, Rozin, Bauer, and Catanese (2003) examined the importance of food as a source of pleasure versus concerns about food associated with weight gain and health. The following results are similar to those obtained in the study. The scores are a measure of concern about the negative aspects of eating.

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a. Based on these results, is there a significant difference between the attitudes for males and for females? Use a two-tailed test with α = .05.

b. Compute r2, the percentage of variance accounted for by the gender difference, to measure effect size for this study.

c. Write a sentence demonstrating how the result of the hypothesis test and the measure of effect size would appear in a research report.

a.

To determine

To find: Whetherthere is a significant difference between the attitudes of males and females using two-tailed testat α=0.05.

Explanation

Given info:

Two samples of males and females each with size 9 and 15 have means 33 and 42 respectively. Similarly, both of them have sum of squared difference (SS) equal to 740 and 1240 respectively.

Calculations:

Step 1:

Stating the testing hypotheses:

Null Hypothesis

H0:μ1μ2=0

Alternate Hypothesis

H1:μ1μ20

Step 2: For the given sample, the t-statistics will have degrees of freedom equals:

df=n1+n22=9+152=22

For a two-tailed test with α=0.05 and df=22, the critical value (CV)  is obtained from the t-table as t=±2.074

Step 3: t-statistics is calculated using formula:

t=(M1M2)(μ1μ2)sM1M2

But before that calculate pooled variance, sp2, using formula:

sp2=SS1+SS2df1+df2

Substitute 740for SS1, 1240 for SS2 and 8 for df1 and 14 df2 in the above formula

sp2=740+12408+14=90

Now

b.

To determine

To Find: The value of r2 to measure effect size for the mean difference 

c.

To determine

To describe: The outcome of the hypothesis test and the measure of the effect size.

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