A tire manufacturer has been producing tires with an average life expectancy of 26,000 miles. Now the company is advertising that its new tires' life expectancy has increased. In order to test the legitimacy of the advertising campaign, an independent testing agency tested a sample of 6 of their tires and has provided the following data. Life Expectancy (In Thousands of Miles) 28 27 25 28 29 25
a. Determine the mean and the standard deviation.
b. At 99% confidence using the critical value approach, test to determine whether or not the tire company is using legitimate advertising. Assume the population is normally distributed.
c. Repeat the test using the p-value approach.
a. x = 27, s = 1.67
b. Ho: ? < 26000
Ha: ? > 26000
Since t = 1.47 < 3.365, do not reject Ho and conclude that there is insufficient evidence to support the manufacturer's claim.
c. p-value > 0.1; do not reject Ho
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