# Statistics Problem Set and Signficance Levels

5. 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 is59,500 miles. Is Crosset's experience different from that claimed by the manufacturer at the .05 significance level?

6. The MacBurger restaurant chain claims that the waiting time of customers for service is normally distributed, with a mean of 3 minutes and a standard deviation of 1 minute. The quality-assurance department found in a sample of 50customers at the Warren RoadMacBurger that the mean waiting time was 2.75 minutes. At the .05 significance level, can we conclude that the mean waiting time is less than 3 minutes?

7. A recent national survey found that high school students watched an average (mean) of 6.8DVDs per month. A random sample of 36 college students revealed that the mean number of DVDs watched last month was 6.2, with a standard deviation of 0.5. At the .05 significance level, can we conclude that college students watch fewer DVDs a month than high school students?

8. At the time she was hired as a server at the Grumney Family Restaurant, Beth Brigden was told, "You can average more than $20 a day in tips." Over the first 35 days she was employed at the restaurant, the mean daily amount of her tips was $24.85, with a standard deviation of $3.24. At the .01 significance level, can Ms. Brigden conclude that she is earning an average of more than $20 in tips?

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#### Solution Preview

Notations: n = sample size, Ïƒ = population Standard Deviation(S.D), s = sample S.D, x = sample mean, Î¼0 = population mean

Please complete the following exercises using Excel with a DETAILED explanation as to what functions you used. Thank you.

5. Solution:

Let Î¼ be the mean mileage the tire can be driven before the tread wears. Then to test the hypothesis Î¼ = 60000 Vs Î¼ â‰ 60000.

The test statistic is

See attached

Here Î¼_0 = 60000, Ïƒ = 5000, n =48, x ...

#### Solution Summary

Solution contains the application of testing of hypothesis.