Question

A manufacturer of AAA batteries wants to estimate the mean life expectancy of the batteries. A sample of 25 such batteries shows that the distribution of life expectancies is roughly normal with a mean of 44.25 hours and a standard deviation of 2.25 hours. Construct a 98% confidence interval for the mean life expectancy of all the AAA batteries made by this manufacturer

Answer 1

Solution :

Given that,

t /2,df = 2.492

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

= 2.492 * (2.25 / 25)

Margin of error = E = 1.12

The 98% confidence interval estimate of the population mean is,

- E < < + E

44.25 - 1.12 < < 44.25 + 1.12

43.13 < < 45.37

(43.13 , 45.37)