Question

The ages of a group of 135 randomly selected adult females have a standard deviation of 17.9 years. Assume that the ages of female statistics students have less variation than ages of females in the general​ population, so let sigmaequals17.9 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

=17.9

Margin of error, MoE =1.5

At 95% confidence level, for a two-tailed case, the critical value of Z is, Z_crit =1.96

We know that, MoE =Z_crit*n =(Z_crit^*/MoE)² =(1.96*17.9/1.5)² =547.061​​​​​​. Rounding to the next integer, n =548

So, 548 female statistics student ages must be obtained in order to estimate the mean age of all female statistics​ students.

It seems reasonable to assume that the ages of female statistics students have less variation than ages of females in the general​ population because the females in the general population are relatively too large and so, it's variation will be more than female Statistics students who are relatively less.