SOLUTION: The manufacturer of a particular all-season tire claims that the tires last for 22,000 miles. After purchasing the tires you discover that yours did not last the full 22,000 mile
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Question 1035368: The manufacturer of a particular all-season tire claims that the tires last for 22,000 miles. After purchasing the tires you discover that yours did not last the full 22,000 miles. Suppose that a sample of 100 tires made by that manufacturer lasted on average 21,819 miles with a sample standard deviation of 1,295 miles. Is there sufficient evidence to refute the manufacturer’s claim that the tires last 22,000 miles? Let a = 0.05. Assume that the population standard deviation is s = 1300.
a. Define the null and alternative hypotheses.
b. Find the appropriate rejection region.
c. Compute the test statistic.
d. What is your conclusion? Explain.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The manufacturer of a particular all-season tire claims that the tires last for 22,000 miles. After purchasing the tires you discover that yours did not last the full 22,000 miles. Suppose that a sample of 100 tires made by that manufacturer lasted on average 21,819 miles with a sample standard deviation of 1,295 miles. Is there sufficient evidence to refute the manufacturer’s claim that the tires last 22,000 miles? Let a = 0.05. Assume that the population standard deviation is s = 1300.
a. Define the null and alternative hypotheses.
Ho: u >= 22000 (claim)
Ha: u < 22000
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b. Find the appropriate rejection region.
z < -1.645
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c. Compute the test statistic.
z(21819-22000)/(1300/sqrt(100) = -1.3923
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d. What is your conclusion? Explain.
Since the test stat is not in the reject interval,
fail to reject Ho. The test results support the claim.
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Cheers,
Stan H.
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