Question

The Chekzar Rubber Company, in financial difficulties because of a poor reputation for product quality, has come out with an ad campaign claiming that the mean lifetime for Chekzar tires is 60,000 miles in highway driving. The editors of a consumer magazine are skeptical, and believe that it is actually less than 60,000 miles. They randomly purchase 36 of the tires and test them in highway use. The mean tire life in the sample is 58,341.69 miles, with a sample standard deviation of 3632.53 miles. If the population of tire life is approximately normal, what conclusion can the editors draw?

Answer 1

a.

Null hypothesis: mean lifetime >= 60,000 miles

Alternate hypothesis: mean lifetime < 60,000 miles

We know that:

Assumed population mean, mu= 60,000 miles

Sample mean, xbar= 58,341.69 miles

Sample standard deviation, s= 3,632.53 miles

Sample size, n= 36

Thus, the test t statistic= (xbar-mu) / s/sqrt(n)

= (58341.69- 60000) / 3632.53/sqrt(36)

= -1658.31/ 605.4217

= -2.739099

T critical value, 35 degrees of freedom at

1% significance= -2.437723

5% significance= -1.689572

10% significance= -1.306212

Thus, since the test statistic is outside the acceptance region, we reject the null hypothesis. The mean lifetime is significantly different from 60,000 miles.

b.

Based on our conclusion, we could have made a type I error.

A type 1 error is the incorrect rejection of the null hypothesis.

This would mean that the null hypothesis should not have been rejected. In our example, this means that the mean lifetime is actually not significantly different from 60,000 miles. Due to a 'by-chance' scenario, we got a sample as extreme as this.