# Test a hypothesis

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The manufacturer of the X-15 steel-belted radial truck tire claims that the mean mileage the tire

can be driven before the tread wears out is 60,000 miles. The standard deviation of the mileage is

5,000 miles. The Crosset Truck Company bought 48 tires and found that the mean mileage for

their trucks is 59,500 miles. Is Crosset's experience different from that claimed by the manufacturer

at the .05 significance level?

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##### Solution Summary

The solution contains detailed explanation of testing hypotheses using the five-step procedure.

###### Education

- BSc , Wuhan Univ. China
- MA, Shandong Univ.

###### Recent Feedback

- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
- "excellent work"
- "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
- "Thank you"
- "Thank you very much for your valuable time and assistance!"

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