Question

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 2 grams. how many mice must be weighed so that a 95% confidence interval will have margin of error of 0.5 grams. write only an integer as your as your answer.

Answer 1

Solution

standard deviation =   =2

Margin of error = E = 0.5

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96 ( Using z table ( see the 0.025 value in standard normal (z) table corresponding z value is 1.96 )

sample size = n = [Z_/2* / E] ²

n = ( 1.96* 2 /0.5 )²

n =61.46

Sample size = n =62