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Proportion of Sample Who Enjoy Shopping

Sample question:
A sample of 500 shoppers were selected in a large metropolitan to determine various information concerning consumer behavior. Among the questions asked was, "Do you enjoy shopping for clothing?"

The results are summarized in the following contigency table:

Enjoy Shopping for Clothing MALE FEMALE TOTAL
YES 136 224 360

NO 104 36 140

TOTAL 240 260 500

a) Is there evidence of a significant difference between the proportion males and females who enjoy shopping for clothing at the 0.01 level of significance?
b) Determine the p-value in (a) and interpret its meaning
c) What are your answers to (a) and (b) if 206 males enjoyed shopping for cloting and 34 did not?

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Answers

a. Is there evidence of a significant difference between the proportion of males and females who enjoy shopping for clothing at the 0.01 level of significance?

The null hypothesis tested is

H0: There is no significant difference between the proportion of males and females who enjoy shopping for clothing.

The alternative hypothesis is

H1: There is significant difference between the proportion of males and females who enjoy shopping for clothing.

The test statistic used is x^2 = sum of (O - E) / E = 0.010648266 where O is the observed frequency and E is the expected frequency.

The Expected frequencies are given below. They are calculated using the formula, , where Ri , ith row total, Cj jth column total and G is the grand Total.

Rejection Criteria: Reject the null hypothesis, if the calculated value of chi square is greater than the critical value of Chi square with 1 d.f. at 0.01 significance level.

The observed and expected frequencies are given in the tab Qn. a.

Test statistic, x^2 = sum of (O - E) / E = ...

Solution Summary

Level of Significance for Proportion of Sample Who Enjoy Shopping

$2.19