Question

A spark plug manufacturer claimed that a new manufacturing procedure has changed the mean life of their plugs from 22,100 miles. Assume that the life of the spark plugs follows the normal distribution. A fleet owner purchased a large number of sets. A sample of 18 sets revealed that the mean life was 23,400 miles and the standard deviation was 1,500 miles. Is there enough evidence to substantiate the manufacturer’s claims at the 0.05 significance level?

Answer 1

H₀: = 22100

H₁: 22100

The test statistic t = ()/(s/)

                           = (23400 - 22100)/(1500/sqrt(18))

                           = 3.68

At 0.05 significance level the critical values are t_{0.025, 17} = +/- 2.110

Since the test statistic value is greater than the upper critical value (3.68 > 2.110), we should reject the null hypothesis.

So at 0.05 significance level there is sufficient evidence substantiate the manufacture's claim.