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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
50
0 if you use the Z test?
9.13
Do students at your school study more than, less than, or about the same as students at other business schools? BusinessWeek reported that at the top 50 business schools, students studied an average of 14.6 hours per week (data extracted from “Cracking the Books,” Special Report/Online Extra,
www.businessweek.com
, March
19
, 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 BusinessWeek.
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?
9.15
The Manager of a paint supply store wants to determine whether the mean amount of paint contained in 1-gallon cans purchased forma nationally known manufacturer is actually 1 gallon. You know from the manufacture’s specifications that he standard deviation of the amount of paint is 0.02 gallon. You select a random sample of 50 cans, and the mean amount of paint per 1-gallon can is 0.995 gallon.
a. Is there evidence that the mean amount is different from 1.0 gallon (use = 0.01)
b. Compute the p-value and interpret its meaning.
c. Construct a 99% confidence interval estimate of the population mean amount of paint.
d. Compare the results of (a) and (c). What conclusions do you reach?
9.27
In New York State, savings banks are permitted to sell a form of life insurance called savings bank life insurance (SBLI). The approval process consists of underwriting, which includes a review of the application, a medical information bureau check, possible requests for additional medical information and medical exams, and a policy compilation stage in which the policy pages are generated and sent to the bank for delivery. The ability to deliver approved polices to customers in a timely manner is critical to the profitability of this services. During a period of one month, a random sample of 27 approved polices is selected, and the total processing time, in days, is recorded (and stored in Insurance):
|
73 |
19 |
16 |
64 |
28 |
31 |
90 |
60 |
56 |
22 |
18 |
||||
|
45 |
48 |
17 |
91 |
92 |
63 |
50 |
51 |
69 |
a. In the past, the mean processing time was 45 days. At the 0.05 level of significance, is there evidence that he mean processing tiem has changed from 45 days?
b.
What assumption about the population distribution is needed in order to conduct the t test in (a).
c. Construct a boxplot or a normal probability plot to evaluate the assumption made in (b).
d. Do you think that the assumption needed in order to conduct the t test in (a) is valid? Explain.
