A tire manufacturer has a 60,000-mile warranty for tread life. The manufacturer considers the overall tire quality to be acceptable if less than 8% are worn out at 60,000 miles. The manufacturer tests 250 tires that have been used for 60,000 miles. They find that 15 of them are worn out. With this data, we test the following hypotheses at the 5% significance level. H?: The proportion of tires that are worn out after 60,000 miles is equal to 0.08. H?: The proportion of tires that are worn out after 60,000 miles is less than 0.08. The p-value is 0.15. Which conclusion is correct? Accept H? Fail to reject H? Reject H?
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08. \[ H_o: p = 0.08 \] - Alternative Hypothesis (\(H_a\)): The proportion of tires that are worn out after 60,000 miles is less than 0.08. \[ H_a: p < 0.08 \] - Significance level (\(\alpha\)): 0.05 Show more…
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A tire manufacturer has a 60,000 mile warranty for tread life. The manufacturer considers the overall tire quality to be acceptable if less than 5% are worn out at 60,000 miles. The manufacturer tests 250 tires that have been used for 60,000 miles. They find that 3.6% of them are worn out. With this data, we test the following hypotheses. H0: The proportion of tires that are worn out after 60,000 miles is equal to 0.05. Ha: The proportion of tires that are worn out after 60,000 miles is less than 0.05. What assumption about the sample underlies the hypothesis test? The sample comes from a population of tires where 250 are used for 60,000 miles. The sample comes from a population of 250 tires that have a 60,000 mile warranty. The sample comes from a population of tires with 60,000 miles where 3.6% of the tires are worn out. The sample comes from a population of tires with 60,000 miles where 5% of tires are worn out.
Madhur L.
A tire manufacturer has a 60,000 mile warranty for tread life. The company wants to make sure the average tire lasts longer than 60,000 miles. The manufacturer tests 250 tires and finds the mean life for these tires to be 64,500 miles. What is the alternative hypothesis being tested in this example? The proportion of tires that are worn out after 60,000 miles is greater than 1/2. The mean tire life is equal to 64,500 miles. The mean tire life is less than 60,000 miles. The mean tire life is greater than 60,000 miles.
David N.
Conduct the hypothesis test and provide the test statistic and the P-value and/or critical value, and state the conclusion. A classic story involves four carpooling students who missed a test and gave as an excuse a flat tire. On the makeup test, the instructor asked the students to identify the particular tire that went flat. If they really didn't have a flat tire, would they be able to identify the same tire? The author asked 41 other students to identify the tire they would select. The results are listed in the following table (except for one student who selected the spare). Use a 0.05 significance level to test the author's claim that the results fit a uniform distribution. What does the result suggest about the likelihood of four students identifying the same tire when they really didn't have a flat? $$\begin{array}{lc|c|c|c} \hline \text { Tire } & \text { Left Front } & \text { Right Front } & \text { Left Rear } & \text { Right Rear } \\ \hline \text { Number Selected } & 11 & 15 & 8 & 6 \\ \hline \end{array}$$
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