Question

A researcher is interested in estimating the mean level of a water pollutant for a county in CA within 15 mg/l. As part of the initial research, the researcher conducts a pilot study and finds the sampled standard deviation to be 7 mg/l. What is the minimum sample size required if the researcher wants to be confident at the 95% level?

Answer 1

Solution :

Given that,

Population standard deviation = = 7

Margin of error = E = 1.5

At 95% confidence level the z is,

= 1 - 95%

= 1 - 0.95 = 0.05

/2 = 0.025

Z_/2 = 1.96

sample size = n = [Z_/2* / E] ²

n = [ 1.96 * 7 / 1.5 ]²

n = 83.66

Sample size = n = 84