Question

1. A government investigator plans to test for the mean quantity of a particular pollutant that a manufacturer is dumping into a river each day. She needs an estimate that is within 50 grams at the 95% confidence level. If previous measurements indicate that the variance is approximately 21,800 grams, how many days should she include in the sample?

Answer 1

Solution :

Given that,

Population standard deviation = = 21800 =147.6482 grams

Margin of error = E = 50 grams

At 95% confidence level

= 1-0.95% =1-0.95 =0.05

/2 =0.05/ 2= 0.025

Z/2 = Z_{0.025 = 1.960}

Z/2 = 1.960  

sample size = n = [Z_/2* / E] ²

n = [ 1.960*147.6482 /50) ²

n = 33.5

Sample size = n = 34 days