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.