Chapter 4.5, Problem 15E

In Exercises $9-22$, round off your answers (sample proportions and margins of error) to three decimal places (a tenth of a percent).

A survey asked, "Do you prefer showering or bathing?" Of the 1, 220 American men surveyed, 1, 049 preferred showering, and 171 preferred bathing. In contrast. 1, 043 of the 1, 490 American women surveyed preferred showering, and 447 preferred bathing.*

a. Determine the sample proportion of American men who prefer showering.

b. Determine the sample proportion of American women who prefer showering.

c. With a $95\%$ level of confidence, find the margin of error associated with the sample proportions.