Question

The ages of a group of 130 randomly selected adult females have a standard deviation of 16.2 years. Assume that the ages of female statistics students have less variation than ages of females in the general population, so let σ=16.2 years for the sample size calculation. How many female statistics student ages must be obtained in order to estimate the mean age of all female statistics students? Assume that we want 95% confidence that the sample mean is within one-half year of the population mean. Does it seem reasonable to assume that the ages of female statistics students have less variation than ages of females in the general population?

Answer #1

(a)

Question:

How many female statistics student ages must be obtained in order to estimate the mean age of all female statistics students?

Sample Size (n) is given by:

Given :

= 0.05

From Table, critical values of Z = 1.96

= 16.2

e = 1.5

Substituting, we get:

So,

Answer is:

**449**

(b)

Question:

Does it seem reasonable to assume that the ages of female statistics students have less variation than ages of females in the general population?

Since Sample Size = n = 130 > 30, Large Sample, by Central Limit Theorem, it seems reasonable to assume that the ages of female statistics students have less variation than ages of females in the general population.

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