Question

You are a researcher studying the lifespan of a certain species of bacteria. A preliminary sample of 40 bacteria reveals a sample mean of ¯ x = 64 hours with a standard deviation of s = 4.4 hours. You would like to estimate the mean lifespan for this species of bacteria to within a margin of error of 0.75 hours at a 99% level of confidence. What sample size should you gather to achieve a 0.75 hour margin of error? Round your answer up to the nearest whole number.

Answer 1

We have given here,              
              
Population standard deviation =4.4 hours
Margin of error =E=0.75 hours
Level of significance =   1-0.99=0.01
Z critical value is (by using Z table)=2.576
Sample size formula is               


= 228.39

Sample size