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Calculus and Above# 9.3 If you use a 0.10 level of significance in a two-tail hypothesis

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test, what is your decision...

9.3 If you use a 0.10 level of significance in a two-tail hypothesis test, what is your decision rule for rejecting a null hypothesis that the population mean equals 500 if you use the Z test?

9.13 Do business seniors at your school prepare for class more than, less than, or about the same as business seniors at other schools? The National Survey of Student Engagement (NSSE) found that business seniors spent a mean of 14 hours per week preparing for class. (Source: A Fresh Look at Student Engagement Annual Results 2013, available at bit.ly/1j3Ob7N.)

a. State the null and alternative hypotheses to try to prove that the mean number of hours preparing for class by business seniors at your school is different from the 14-hour-per-week benchmark reported by the NSSE.

b. What is a Type I error for your test?

c. What is a Type II error for your test?

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.

I do not need 9.14 answered just providing based on question 9.15

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?

9.25 A manufacturer of chocolate candies uses machines to package candies as they move along a filling line. Although the packages are labeled as 8 ounces, the company wants the pack-ages to contain a mean of 8.17 ounces so that virtually none of the packages contain less than 8 ounces. A sample of 50 packages is selected periodically, and the packaging process is stopped if there is evidence that the mean amount packaged is different from 8.17 ounces. Suppose that in a particular sample of 50 packages, the mean amount dispensed is 8.159 ounces, with a sample standard deviation of 0.051 ounce.

a. Is there evidence that the population mean amount is different from 8.17 ounces? (Use a 0.05 level of significance.)

b. Determine the p-value and interpret its meaning.

9.49 You are the manager of a restaurant that delivers pizza to college dormitory rooms. You have just changed your delivery process 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?

9.13 Do business seniors at your school prepare for class more than, less than, or about the same as business seniors at other schools? The National Survey of Student Engagement (NSSE) found that business seniors spent a mean of 14 hours per week preparing for class. (Source: A Fresh Look at Student Engagement Annual Results 2013, available at bit.ly/1j3Ob7N.)

a. State the null and alternative hypotheses to try to prove that the mean number of hours preparing for class by business seniors at your school is different from the 14-hour-per-week benchmark reported by the NSSE.

b. What is a Type I error for your test?

c. What is a Type II error for your test?

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.

I do not need 9.14 answered just providing based on question 9.15

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?

9.25 A manufacturer of chocolate candies uses machines to package candies as they move along a filling line. Although the packages are labeled as 8 ounces, the company wants the pack-ages to contain a mean of 8.17 ounces so that virtually none of the packages contain less than 8 ounces. A sample of 50 packages is selected periodically, and the packaging process is stopped if there is evidence that the mean amount packaged is different from 8.17 ounces. Suppose that in a particular sample of 50 packages, the mean amount dispensed is 8.159 ounces, with a sample standard deviation of 0.051 ounce.

a. Is there evidence that the population mean amount is different from 8.17 ounces? (Use a 0.05 level of significance.)

b. Determine the p-value and interpret its meaning.

9.49 You are the manager of a restaurant that delivers pizza to college dormitory rooms. You have just changed your delivery process 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?

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