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# Testing hypotheses about the population mean

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Fast Service, a chain of automotive tune-up shops, advertises that its personnel can change the oil, replace the oil filter, and lubricate any standard automobile in 15 minutes, on the average. The National Business Bureau received complaints from customers that service takes considerably longer. To check the fast service claim, the Bureau had service done on 21 unmarked cars. The mean service time was 18 minutes and the standard deviation of the sample was 1 minute. Use the .05 significance level to check the reasonableness of the fast service claim.

##### Solution Summary

The solution contains detailed explanation of testing whether the population mean is different from a given value.

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Solution. Let X be the service time. We can assume that X follows normal distribution, X~N(a, b^2), where a is the mean of X and b is the standard deviation of X. Define Null hypothesis:

Ho: a=15 (minutes)
H1: a is not equal 15.

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• 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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