The ages of a group of 144 randomly selected adult females have a standard devia

Question

The ages of a group of 144 randomly selected adult females have a standard deviation of 18.8 years. Assume that the ages of female statistics students have less variation than ages of females in the general population, so let sigma=18.8 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 90% 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? The ages of a group of 144 randomly selected adult females have a standard deviation of 18.8 years. Assume that the ages of female statistics students have less variation than ages of females in the general population, so let sigma=18.8 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 90% 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?

Explanation / Answer

Solution

Let X = age of female statistics students.

We assume X ~ N(µ, ?2) where ? is assumed to be 18.8 [given ‘so let sigma=18.8 years for the sample size calculation’]

‘we want 90% confidence that the sample mean is within one-half year of the population mean.’ => P{| (Xbar - µ) | ? ½ ] = 0.9

=> P[{?n|(Xbar - µ)|/18.8} ? {(?n)(½)/18.8}] = 0.9

=> {(?n)(½)/18.8} = Z0.05 i.e., upper 5% point of N(0, 1)

[because {?n|(Xbar - µ)|/18.8} ~ N(0, 1)]

So, we have, {(?n)(½)/18.8} = 1.645 [using Excel Function of N(0, 1)]

Or (?n) = 37.6 x 1.645

            = 61.852 or

n = 3825 ANSWER 1

It does it seem reasonable to assume that the ages of female statistics students have less variation than ages of females in the general population because the group of female statistics students is much more homogenous than general female population. ANSWER 2

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