What sample size should you gather to achieve a 0.75 hour margin of error?

Question

A researcher studying the lifespan of a certain species of bacteria. A preliminary sample of 40 bacteria reveals a sample mean of  hours with a standard deviation of  hours. He would like to estimate the mean lifespan for this species of bacteria to within a margin of error of 0.75 hours at a 90% level of confidence.What sample size should you gather to achieve a 0.75-hour margin of error? He would need to sample Incorrect_____ bacteria.

Answer 1

E = margin of error

z-critical = z-score for desired level of confidence

s = given standard deviation

n = sample size to be computed

E = z-critical * s/n^1/2

n^1/2 = z-critical * s/E

n = (z-critical*s/E)^2

n = (z-critical * s/E)^2, where z-critical is 1.645 for a 90% confidence level, s is given as 4.4, and 0.75 is given as the margin of error.

n = (1.645*4.4/0.75)^2 = 93.14, so would need 94 bacteria.