Question

The ages of a group of 135 randomly selected adult females have a standard deviation of 18.3 years. Assume that the ages of female statistics students have less variation than ages of females in the general​ population, so let sigmaequals18.3 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.

Answer 1

Answer:

Therefore, the number of female statistics student ages that must be obtained in order to estimate the mean age of all female statistics student is 3625 female statistics student

Step-by-step explanation:

Here, we have

$n = \left (\frac{(z_{\alpha/2}) (\sigma) }{E} \right )^{2}$

Where:

n = Required sample size

σ = Standard deviation = 18.3

E = Margin of error = 1/2 year

$z_{\alpha /2}$ = Critical score from the confidence level = 1.645

Therefore,

$n = \left (\frac{(1.645) (18.3) }{\frac{1}{2} } \right )^{2} = 3624.88$

Therefore, the number of female statistics student ages that must be obtained in order to estimate the mean age of all female statistics student = 3625 female statistics student.