You are a researcher studying the lifespan of a certain species of bacteria. A preliminary sample of 30 bacteria

Question

You are a researcher studying the lifespan of a certain species of bacteria. A preliminary sample of 30 bacteria reveals a sample mean of ¯x=74x¯=74 hours with a standard deviation of s=5s=5 hours. You would like to estimate the mean lifespan for this species of bacteria to within a margin of error of 0.45 hours at a 95% level of confidence.

What sample size should you gather to achieve a 0.45 hour margin of error? Round your answer up to the nearest whole number.

n = _____ bacteria

Answer 1

95% confidence, z = 1.96 S = 5 E = 0.45

n = (1.96 x 5 / 0.45)²

^{n = 474}