Question

A particular brand of tires claims that its snow tire averages less than 50,000 miles before it needs to be replaced. From past studies of this tire, the standard deviation is known to be 8,000. A survey of owners of that tire design is conducted. From the 28 tires surveyed, the mean lifespan was 46,500 miles with a standard deviation of 9,800 miles. Using α = 0.05 to test the claim.

Answer 1

The null and alternate hypothesis are:

H0:

Ha:

The test statistic is given by:

Since this is a left-tailed test, so the p-value is given by:

Since p-value is less than 0.05, so we have sufficient evidence to reject the null hypothesis H0.

Thus we can say that .