Question

Life test performed on a sample of 13 batteries of a new model indicated one and average life of 75 months and to a standard deviation of 5 months other battery models produced by similar processes have normally distributed lifespans the 90% confidence interval for the population mean the life of the new model is

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 75

sample standard deviation = s = 5

sample size = n = 13

Degrees of freedom = df = n - 1 = 12

At 90% confidence level the t is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

t _/2,df = t_0.05,12 = 1.782

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

= 1.782 * ( 5/ 13)

= 2.471

The 90% confidence interval estimate of the population mean is,

- E < < + E

75 - 2.471 < < 75 + 2.471

72.529 < < 77.471

The 90% confidence interval for the population mean the life of the new model is (72.529 , 77.471)