Question

The ages of a group of

125125

randomly selected adult females have a standard deviation of

16.116.1

years. Assume that the ages of female statistics students have less variation than ages of females in the general​ population, so let

sigmaσequals=16.116.1

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

9595​%

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 required sample size is

Answer 1

Solution :

Given that,

Population standard deviation = = 16.1

Margin of error = E = 0.5

At 95% confidence level the z is,

= 1 - 95%

= 1 - 0.95 = 0.05

/2 = 0.025

Z/2 = Z0.025 = 1.96  

sample size = n = [Z/2* / E] 2

n = [1.96 * 16.1 /0.5 ]2

n = 3983.12

Sample size = n = 3984

Yes,because statistic students are typically younger than people in the general population.