1. In a recent year, the FCC reported that the mean wait for repairs for AT&T customers was 25.3 hours. In an effort to improve this service, suppose that a new repair service process was developed. This new process when used with a sample of 100 repairs, resulted in a sample mean of 22.3 hours and a sample standard deviation of 8.3 hours.
a. Is there evidence that the population mean amount is less than 25.3 hours? (Use a 0.05 level of significance.)
b. Determine the p-value and interpret its meaning.
2. The U.S. Department of Education reports that 46% of full-time college students are employed while attending college (data extracted from "The Condition of Education 2009," National Center for Education Statistics, nces.ed.gov). A recent survey of 60 full-time students at Miami University found that 29 were employed.
A. Use the five-step p-value approach to hypothesis testing and a 0.05 level of significance to determine whether the proportion of full-time students at Miami University is different than the national norm of 0.46.
B. Assume that the study found that 36 of the 60 full-time students were employed and repeat (a). Are the conclusions the same?
3. Studies conducted by a manufacturer of "Boston" and "Vermont" asphalt shingles have shown products weight to be a major factor in the customers perception of quality. Moreover, the weight represents the amount of raw materials being used and is therefore very important to the company from a cost standpoint. The last stage of the assembly line packages the shingles before the packages are placed on wooden pallets. Once a pallet is full.(It holds 16 squares of shingles) The data file contains the weight in pounds for a sample of 368 pallets of Boston Shingles and 330pallets of Vermont shingles.
a. For the Boston shingles, is there evidence that the population mean weight is different from 3,150 pounds.
b. Interpret the meaning of the p-value in (a)
c. For the Vermont shingles, is there evidence that the population mean weight is different from 3700 pounds.
d. Interpret the meaning of the p-value in(c).
e. In (a) through (d), do you have to worry about the normality assumption? Explain.