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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. 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?
Question #2
The manager of a paint supply store wants to determine whether the mean amount of paint contained in 1-gallon cans purchased form a nationally known manufacturer’s specifications that the 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 α=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 your reach?
Question #3
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 policies to customers in a timely manner is critical to the profitability of this service to the bank. During a period of one month, a random sample of 27 approved policies was selected, and the total processing time, in days, was as shown below.
73 19 16 64 28 28 31 90 60 56 31 56 22 18 45 48 17 17 17 91 92 63 50 51 69 16 17
a)In the past, the mean processing time was 45 days. At the 0.05 level of significance, is there evidence that the mean processing time 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.
Question #4
According to a recent study, when shopping online for luxury goods, men spend a mean of $2,401, whereas women spend a mean of $1,527. Suppose that the study was based on a sample of 600 men and 700 females, and the standard deviation of the amount spent was $1,200 for men and $1,000 for women.
a) State the null and alternative hypothesis if you want to determine whether the mean amount spent is higher for men than for women.
b) In the context of this study, what is the meaning of the Type I error?
c) In the context of this study, what is the meaning of the Type II error?
d) At the 0.01 level of significance, is there evidence that the mean amount spent is higher for men than for women?
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