Question

The ages of a group of 131 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 sigmaequals18.9 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 99​% 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

___ (Round up to the nearest whole number as​ needed.)

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

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

B. No, because statistics students are typically older than people in the general population.

C. Yes, because statistics students are typically older than people in the general population.

D. No, because there is no age difference between the population of statistics students and the general population.

Answer 1

Solution :

Given that,

Population standard deviation = = 18.9

Margin of error = E = 0.5

At 99% confidence level the z is,

= 1 - 99%

= 1 - 0.99 = 0.01

/2 = 0.005

Z/2 = Z0.005 = 2.576

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

n = [ 2.576 * 18.9 / 0.5 ]2

n = 9481.46

Sample size = n = 9482

correct option is = A

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