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 compared to 44% of the males. (Data extracted from "Split Decision on Clothes Shopping," USA Today, January 28, 2011, p. IB.) The sample sizes of males and females were not provided. Suppose that of 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.
a. Is there evidence of a difference between males and females in the proportion who enjoy shopping for clothing for themselves at the 0.01 level of significance?
b. Find the /7-value in (a) and interpret its meaning.
c. Construct and interpret a 99% confidence interval estimate for the difference between the proportion of males and females who enjoy shopping for clothing for themselves.
d. What are your answers to (a) through (c) if 218 males enjoyed shopping for clothing for themselves?