How would this company estimate the percentage of people in the U.S. who use electricity to heat their homes?

Question

The utility company wishes to estimate the percentage of people in the U.S. who use electricity to heat their homes. Past data indicate that 154 out of 700 customers surveyed used electricity to heat their homes. If the company wishes to be 98% confident to within 3%, how large a sample would be needed?



a. 516

b. 733

c. 854

d. 1036

e. 1266

f. 1503

g. 2066

h. none of these

Answer 1

.03 = 2.575*sqrt(.22*.78/n)
.03/2.575 = sqrt(.22*.78/n)
.0116504854 = sqrt(.22*.78/n)
.0116504854^2 = .22*.78/n
n = .22*.78/.0116504854^2 = 1264.239167 = 1265 (e)

Answer 2

There are table and figures available for such situations.