Question

The ages of a group of 141 randomly selected adult females have a standard deviation of 18.9 years. Assume that the ages of female statistics students have less variation than ages of females in the general​ population, so let σ=18.9years 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?

Answer 1

Solution:

Given ,

= 18.9 ..Population SD

E = 1/2 = 0.5 .. Margin of error

c= 95% =0.95 ...confidence level

Find sample size required.

c = 0.95

= 1- c = 1- 0.95 = 0.05

  /2 = 0.025 and 1- /2 = 0.975

Search the probability 0.975 in the Z table and see corresponding z value

= 1.96

Now, sample size (n) is given by,

= {(1.96* 18.9 )/ 0.5 }^2

=  5489.031744

= 5490 ..(round to the next whole number)

Answer:  5490 female statistics student ages must be obtained in order to estimate the mean age of all female statistics​ students?

Does it seem reasonable to assume that the ages of female statistics students have less variation than ages of females in the general​ population?

Yes .