Round your answer up to the nearest whole number.

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  hours with a standard deviation of   hours.  You would like to estimate the mean lifespan for this species of bacteria to within a margin of error of 0.7 hours at a 99% level of confidence.

What sample size should you gather to achieve a 0.7 hour margin of error? Round your answer up to the nearest whole number.

Answer 1

sample size = (z-critical * s/margin of error)^2

z-critical for 99% level of confidence is the z-score corresponding to 99.5 percentile or 0.995 probability = 2.58.

we are given s=6.8 and margin of error = 0.7, so we can plug those values into the equation to compute sample size, rounding up to the nearest whole number:

sample size = (2.58 * 6.8/0.7)^2 = 628.14 ~ 629

Answer 2

Oo, bacteria.~~~

Okay, so let's look at the formula for a confidence interval for a population mean: x-bar ± error.

The error, since we are looking at a sample of bacteria, is E = z_a/2(s/√n).

Solving this for n, we get: n = (z_a/2(s)/E)². As you can see, the process for determining an appropriate sample size does not depend on x-bar. When you do a problem of this nature, you always round up n in order to preserve the desired accuracy. Rounding down compromises that accuracy.

Substitute the values z_a/2 = 2.576 (the z-quartile used for 99% CI's for population mean), s = 6.8, and E = 0.7. Plugging these values into the formula, we find that n ≈ 626.200576. Round up: n = 627.

Gather a sample of 627 bacteria to achieve a 0.7 hour margin of error.