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The ages of a group of 135 randomly selected adult females have a standard deviation of...

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?

Expert Solution

Let n be the size of the sample of female statistics students that is needed to estimate with 95% confidence that the sample mean is within one-half year of the population mean.

The population standard deviation of the age of female statistics students is less than 17.9 years. But we will assume it to be 17.9 years

is the standard deviation of the age of female statistics students

The standard error of mean for a sample size of n is

We need the critical value for 95% confidence interval. The significance level is

The right tail critical value is

Using the standard normal tables we can find that for z=1.96, P(Z<1.96) = 0.975

Hence

Lastly we want to estimate sample mean is within one-half year of the population mean. This means that the margin of error for 95% confidence interval is 0.5 years (one-half year)

The margin of error is

That is we need a sample of size 4924

ans: 4924 female statistics student ages must be obtained in order to estimate the mean age of all female statistics students.

The females statistics students are likely to belong to a narrower age band, compared to adult females in the general population (age of an adult female in general population may go as high or higher than 100 years, where as a female statistics student is not likely to be 100 year old) .

Hence it is reasonable to assume that the ages of female statistics students have less variation than ages of females in the general population.

milcah answered 1 year ago

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