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 of 5 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 answer.

Answer 1

Solution

standard deviation = =5

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 = Z0.025 = 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*5 / 0.5 )2

n =384.16

Sample size = n =384