Question

Can you please explain me this question? Thanks!

A manufacturer of AAA batteries wants to estimate the mean life expectancy of the batteries. A sample of 20 such batteries shows that the distribution if life expectancies is roughly normal with a sample mean of 32.5 and a sample standard deviation of 2.75 hours. Construct a 95% confidence interval for the mean life expectancy of AAA batteries made by this manufacturer.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 32.5

sample standard deviation = s = 2.75

sample size = n = 20

Degrees of freedom = df = n - 1 = 19

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t _/2,df = t_0.025,19 = 2.093

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

= 2.093 * (2.75 / 20)

= 1.287

The 95% confidence interval estimate of the population mean is,

- E < < + E

32.5 - 1.287 < < 32.5 + 1.287

31.213 < < 33.787

A  95% confidence interval for the mean life expectancy of AAA batteries made by this manufacturer is,

(31.2 , 33.8)