Question

A researcher states that the life expectancy of mice can be extended by up to 25% when about 40% of the calories in their diet are reduced from the time they are weaned. The restricted diet is enriched to normal levels with vitamins and proteins. Assuming that it is known from previous studies that σ = 6.1 months, how many mice should be included in the sample to have 99% confidence that the expected half-life of the sample will be within 2.3 months from the population mean for all mice subject to the reduced diet?

Important note: Use the critical value rounded to 3 decimal places and your answer to the largest integer.

Write the answer with 4 decimals.

Answer 1

Solution :

Z_$\alpha$/2 = Z_0.005 = 2.576  

sample size = n = [Z_$\alpha$/2* $\sigma$ / E] ²

n = [ 2.576 * 6.1 / 2.3 ]²

n = 46.67

Sample size = n = 47 mice.