Question

A random sample of 35 locations in a western state yield an average annual precipitation of 16.7 inches for last year. Suppose the standard deviation is 2.1 inches.

If a meteorologist wants to estimate the rainfall mean within .2 inch with 90% confidence, how large of a sample does she need to take?

Answer 1

Solution :

Given that,

Population standard deviation = = 2.1

Margin of error = E = 0.02

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z_/2 = Z _0.05 = 1.645

sample size = n = (Z_/2* / E) ²

n = (1.645 * 2.1/ 0.02)²

n = 298.3

n = 299

Sample size = 299