Question

Deer mice are small rodents native to North America with body lengths (excluding tails) that are

known to vary approximately Normally, with a mean u = 86 mm and a standard deviation G= 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 u within +/- 2.5 mm with 95% confidence?

Answer 1

To determine the required sample size, we can use the formula:

n = (Z_alpha/2 * sigma / E)^2

where:

Z_alpha/2 = the critical value of the standard normal distribution for a 95% confidence level (1.96)

sigma = the population standard deviation (8 mm)

E = the margin of error (2.5 mm)

Substituting the values, we get:

n = (1.96 * 8 / 2.5)^2

n = 61.31

Rounding up to the nearest whole number, we get n = 62.

Therefore, the researcher would need a sample size of 62 deer mice to estimate the mean body length within +/- 2.5 mm with 95% confidence.

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