Question

5. Scientists want to estimate the mean weight of mice after they have been fed a special diet. From previous studies, it is known that the weight is normally distributed with standard deviation s=3 grams. How many mice must be weighted so that 95% confidence interval will have a margin of error 0.5 grams?                             (8-Pts)

Answer 1

Solution :

Given that,

Population standard deviation = = 3 grams

Margin of error = E = 0.5 grams

At 95% confidence level the z is,

= 1 - 95%

= 1 - 0.95 = 0.05

/2 = 0.025

Z/2 = Z0.025 = 1.96  

sample size = n = [Z/2* / E] 2

n = [1.96 *3 / 0.5 ]2

n = 138.29

Sample size = n = 139 mice