Question

3. Deer mice (adapted from exercise 15.38, 4t ed Baldi & Moore)

3 points
Deer mice are small rodents native to North America with body lengths (excluding tails) that are
known to vary approximately Normally, with a mean ц = 86 mm and a standard deviation o = 8 mm.
A researcher wants to study the effect of habitat food source degradation on deer mouse body
length.
First, however, you want to figure out how many deer mice you would need for successful inference
about the mean u in the population of all deer mice that would ever experience habitat degradation.
What sample size would be needed to estimate y within +/- 2.5 mm with 95% confidence?


I got 62, but the answer is 40, and I can’t figure out what I am doing wrong. Please advise

Answer 1

It's possible that the answer provided is using a different level of confidence than the one specified in the question (95% confidence).

Using the same formula as before, we have:

n = (Z^2 * o^2) / E^2

Substituting the given values, we get:

n = (1.96^2 * 8^2) / 2.5^2 = 61.92

Rounding up to the nearest whole number, we need a sample size of 62 deer mice to estimate the population mean within +/- 2.5 mm with 95% confidence, assuming that the population standard deviation remains the same under habitat food source degradation.

Therefore, it seems like the correct answer should be 62, not 40.