Question

Using = 0.01, test the claim that the mean lifetime of car engines of a particular type is greater than 220,000 miles. In a sample of 23 cars, the mean life was found to be 223,450 miles with standard deviation of 11,500 miles. Use the P-value method and show all work!

Answer 1

Solution :

= 220,000

= 223,450

s = 11,500

n = 23

This is the right  tailed test .

The null and alternative hypothesis is ,

H₀ :   = 220,000

H_a : > 220,000

Test statistic = t =

= ( - ) / s / n

= (223,450 - 220,000) / 11,500 / 23

Test statistic = t = 1.439

degrees of freedom = n - 1 = 23 - 1 = 22

p(T > 1.439) = 1-P (T < 1.439) = 1 - 0.9179

P-value = 0.0821

= 0.01

Fail to the rejected null hypothesis, because p-value > 0.01