# Mathematics

Answer using excel spreadsheet. Must show all formulas

9.15 Suppose that in Problem 9.14, the standard deviation is 1,200 hours.

a. Repeat (a) through (d) of Problem 9.14, assuming a standard deviation of 1,200 hours.

b. Compare the results of (a) to those of Problem 9.14.

9.14 question and Answer:

(9.14 The quality-control manager at a compact flu-orescent light bulb (CFL) factory needs to determine whether the mean life of a large shipment of CFLs is equal to 7,500 hours. The population standard deviation is 1,000 hours. A random sample of 64 CFLs indicates a sample mean life of 7,250 hours.a. At the 0.05 level of significance, is there evidence that the mean life is different from 7,500 hours?b. Compute the p-value and interpret its meaning.c. Construct a 95% confidence interval estimate of the population mean life of the CFLs.d. Compare the results of (a) and (c). What conclusions do you reach?

9.14 Answer:

(a) ZSTAT=7,250-7,5001,000264=-2.0. Because ZSTAT=-2.006 -1.96, reject H0.

(b) p@value=0.0456.

(c) 7,005…m…7,495.

(d) The conclusions are the same.)

9.49 You are the manager of a restaurant that delivers pizza to college dormitory rooms. You have just changed your deliveryprocess in an effort to reduce the mean time between the order and completion of delivery from the current 25 minutes. A sample of 36 orders using the new delivery process yields a sample mean of 22.4 minutes and a sample standard deviation of 6 minutes.

a. Using the six-step critical value approach, at the 0.05 level of significance, is there evidence that the population mean deliv-ery time has been reduced below the previous population mean value of 25 minutes?

b. At the 0.05 level of significance, use the five-step p-value ap-proach.

c. Interpret the meaning of the p-value in (b).

d. Compare your conclusions in (a) and (b).

9.55 According to a recent National Association of Colleges and Employers (NACE) report, 48% of college student internships are unpaid. (Source: “Just 38 Percent of Unpaid Internships Were Subject to FLSA Guidelines,” bit.ly/Rx76M8.) A recent survey of 60 college interns at a local university found that 30 had unpaid internships.a. Use the five-step p-value approach to hypothesis testing and a 0.05 level of significance to determine whether the propor-tion of college interns that had unpaid internships is different from 0.48.b. Assume that the study found that 37 of the 60 college interns had unpaid internships and repeat (a). Are the conclusions the same?