  The ages of a group of 125 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 sigmaσ equal =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?

Question

The ages of a group of 125 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 sigmaσ equal =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?

Step 1

The given information is as follows:

It is given that, the ages of a group of 125 randomly selected adult females have a standard deviation of 16.2 years.

The confidence level is (1–α) = 95%.

From this, the probability value is α = 0.05.

The population standard deviation of ages of females is σ = 16.2 years.

Furthermore, it is given that the estimate of mean age of all statistics students should be within one-half year of the general population. That is, the margin of error should be E = 0.5 years.

Step 2

Obtain the critical value for the given situation:

The critical value corresponding to the given situation is obtained as z(α/2) = 1.96 from the calculation given below:

Step 3

Obtain the number of female statistics students required to estimate the mean age of all statistics students under the given criteria:

Here, 1.96, σ = 16.2 years, E = 0.5 years and z(α/2) = 1.96.

The number of female statistics...

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