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statistics and probability

A research engineer for a tire manufacturer is investigating tire life for a new rubber compound. He has built 16 tires and tested them to end-of-life in a road test. The sample mean and standard deviation are 60,139.7 and 3645.94 kilometers. Compute a 95% tolerance interval on the life of the tires that has confidence level 95%. Compare the length of the tolerance interval with the length of the 95% CI on the population mean. Which interval is shorter? Discuss the difference in interpretation of these two intervals.

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Answer #1

From the given information,

Sample mean

Sample standard deviation

Number of tires

Level of significance

Use the following formula to compute the 95% confidence interval (CI) on mean tire life:

Here,

Substitute the value in the above formula.

Therefore, the 95% confidence interval (CI) on mean tire life is

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