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
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