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=74 hours with a standard deviation of s=5.4 hours. You would like to estimate the mean lifespan for this species of bacteria to within a margin of error of 0.65 hours at a 99% level of confidence.

What sample size should you gather to achieve a 0.65 hour margin of error? Round your answer up to the nearest whole number.

Question

Guest

Mathematics

19 May, 05:46

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=74 hours with a standard deviation of s=5.4 hours. You would like to estimate the mean lifespan for this species of bacteria to within a margin of error of 0.65 hours at a 99% level of confidence.

What sample size should you gather to achieve a 0.65 hour margin of error? Round your answer up to the nearest whole number.

+5

Answers (1)

Know the Answer?

Annabella Eaton · Answer 1

458

Step-by-step explanation:

Margin of error = critical value * standard error

At 99% confidence, the critical value is z = 2.576.

The standard error is σ/√n = 5.4/√n.

Given the desired margin of error is 0.65:

0.65 = 2.576 * 5.4/√n

n = 458