A particular brand of tires claims that its deluxe tire averages at least 50,000 miles before it needs to be replaced. From past studies of this tire, the standard deviation is known to be 8000. A survey of owners of that tire design is conducted. Of the 27 tires in the survey, the average lifespan was 45,900 miles with a standard deviation of 9800 miles. Do the data support the claim at the 5% level? Note: If you are using a Student's t-distribution for the problem, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) State the distribution to use for the test What is the test statistic? What is the p-value? Construct a 95% confidence interval for the true mean. Sketch the graph of the situation. Label the point estimate and the lower and upper bounds of the confidence interval. (Round your lower and upper bounds to the nearest whole number.)
A particular brand of tires claims that its deluxe tire averages at least 50,000 miles before it needs to be replaced. From past studies of this tire, the standard deviation is known to be 8000. A survey of owners of that tire design is conducted. Of the 27 tires in the survey, the average lifespan was 45,900 miles with a standard deviation of 9800 miles. Do the data support the claim at the 5% level?
Note: If you are using a Student's t-distribution for the problem, you may assume that the underlying population is
State the distribution to use for the test
What is the test statistic?
What is the p-value?
Construct a 95% confidence interval for the true mean. Sketch the graph of the situation. Label the point estimate and the lower and upper bounds of the confidence interval. (Round your lower and upper bounds to the nearest whole number.)
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