How large a sample must you take to be 90 % confident that the estimate is within 0.02 of the true proportion of women over age 55 who are widows?

Question

 A recent study indicated that 30% of the 128 women over age 55 in the study were widows. Round up your answers to the next whole number for the following questions.

Answer 1

The 90% confidence interval for the proportion is going to be

p +/- 1.64 sqrt (pq/n)

The 1.64 is the positive Z value for 90% confidence interval

p = 0.3

q = 1 - 0.3 = 0.7

We need 1.64 sqrt (pq/n) < 0.02

You know p,q so solve 1.64 sqrt (pq/n) = 0.02