Question

A survey of 25

randomly selected customers found the ages shown​ (in years). The mean is 31.84 years and the standard deviation is 9.25 years.

​a) Construct a 99​% confidence interval for the mean age of all​ customers, assuming that the assumptions and conditions for the confidence interval have been met.

​b) How large is the margin of​ error?

Answer 1

Solution :

t _/2,df = 2.797

Margin of error = E = t_/2,df * (s /n)

= 2.797 * (9.25 / 25)

Margin of error = E = 5.17

The 99% confidence interval estimate of the population mean is,

- E < < + E

31.84 - 5.17 < < 31.84 + 5.17

26.67 < < 37.01

(26.67 , 37.01)