A survey of 1, 085 adults asked, \"Do you enjoy shopping for clothing for yourse

Question

A survey of 1, 085 adults asked, "Do you enjoy shopping for clothing for yourself?" The results indicated that 51% of the females enjoyed shopping for clothing for themselves as compare to 44% of the males. The sample size of the males and females was not provided. Suppose that off 542 males, 238 said that they enjoyed shopping for clothing for themselves while of 543 females, 276 said that they enjoyed shopping for clothing for themselves. Is there evidence of a significant difference between males and females in the proportion who enjoy shopping for clothing for themselves at the 0.01 level of significance?

Explanation / Answer

Solution:

p1 = 238/542 = 0.4391144

p2 = 276/543 = 0.5082873

Hypothesis Test
Ho: p1=p2

Ha: p1 p2

The test statistic is

Z = (p1-p2)/sqrt(p1*(1-p1)/n1+p2*(1-p2)/n2)

= (0.4391144-0.5082873)/sqrt(0.4391144*(1-0.4391144)/542+0.5082873*(1-0.5082873)/543)

= -2.29

It is a two-tailed test.

Given = 0.01, the critical values are Z/2 = Z(0.005) = -2.58 or 2.58 (from standard normal table)

Since Z=-2.29 is between -2.58 and 2.58, we do not reject Ho.

So we can not conclude that there is evidence of a difference between males and females in the proportion who enjoy shopping for clothing for themseles

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