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##### complete exercises 9.3, 9.13, 9.14, 9.25, 9.48, 9.55

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Question

Complete exercises 9.3, 9.13, 9.14, 9.25, 9.48, 9.55

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 is 500 if you use

the Z test?

9.13 Do students at your school study more than, less

schools, students studied an average of 14.6 hours per

week. (Data extracted from “Cracking the Books,” Special

2007.) Set up a hypothesis test to try to prove that the

mean number of hours studied at your school is different

from the 14.6-hour-per-week benchmark reported by

a. State the null and alternative hypotheses.

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

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

9.14 The quality-control manager at a light bulb

factory needs to determine whether the mean life of

a large shipment of light bulbs is equal to 375 hours. The population

standard deviation is 100 hours. A random sample of

64 light bulbs indicates a sample mean life of 350 hours.

a. At the 0.05 level of significance, is there evidence that

the mean life is different from 375 hours?

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

c. Construct a 95% confidence interval estimate of the population

mean life of the light bulbs.

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 packages 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.

9.48 Southside Hospital in Bay Shore, New York,

commonly conducts stress tests to study the heart

muscle after a person has a heart attack. Members of the diagnostic

imaging department conducted a quality improvement

project with the objective of reducing the turnaround time for

stress tests. Turnaround time is defined as the time from when

a test is ordered to when the radiologist signs off on the test

results. Initially, the mean turnaround time for a stress test was

68 hours. After incorporating changes into the stress-test

process, the quality improvement team collected a sample of

50 turnaround times. In this sample, the mean turnaround

time was 32 hours, with a standard deviation of 9 hours. (Data

extracted from E. Godin, D. Raven, C. Sweetapple, and

F. R. Del Guidice, “Faster Test Results,” Quality Progress,

January 2004, 37(1), pp. 33–39.)

a. If you test the null hypothesis at the 0.01 level of significance,

is there evidence that the new process has reduced

turnaround time?

b. Interpret the meaning of the p-value in this problem.

9.55 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 from 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?

For problems requiring computations, please ensure that your Excel file includes the associated cell computations and/or statistics output; this information is needed in order to receive full credit on these problems.

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