Question

It is calculated that, in order to estimate the true mean amount of money spent by all customers at a grocery store to within $3 with 90% confidence, we require a sample of 180 customers. What sample size would be required to estimate the true mean to within $1 with 90% confidence? Your Answer:

Answer 1

At 90% confidence interval the critical value is z_0.05 = 1.645

Margin of error = 3

or, z_0.05 * = 3

or, 1.645 * = 3

or, = (3 * )/1.645

or, = 24.4676

Margin of error = 1

or, z_0.05 * = 1

or, 1.645 * 24.4676/ = 1

or, n = (1.645 * 24.4676)^2

or, n = 1620