E270 Homework Assignment 10 - Module 10

1.Many consumer groups feel that the U.S. Food and Drug Administration (FDA) drug approval process is too easy and as a result, too many drugs are approved that are later found to be unsafe.On the other hand, a number of industry lobbyists have pushed for a more lenient approval process so that the pharmaceutical companies can get their new drugs approved more easily and quickly.Consider these null and alternative hypothesis:

H0:A new, unapproved drug is unsafe

H1:A new, unapproved drug is safe.

a.Explain both risks involved:Committing a Type I or a Type II error

b.Which type of error are the consumer groups trying to avoid.Explain.

c.Which type of error are the industry lobbyists trying to avoid.Explain.

d.How would it be possible to lower the risk of both Type I and Type II errors?

2.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 8.15 ounces so that the probability of producing a package that contains less than 8 ounces is very small.A sample of 30 packages is selected periodically and weighed, and the packaging process is stopped if there is evidence that the mean packaged amount is statistically different than 8.15 ounces. (They don't want to under-fill or over-fill.)Suppose that a particular sample of 30 packages had a mean weight of 8.13 ounces, with a sample standard deviation of 0.048 ounces.

Use the appropriate hypothesis test to determine if there is evidence that the population mean is different from 8.15 ounces (95% confidence level).

a.State the null and alternative hypothesis.

b.Using both the confidence interval and the p-value, what is your decision regarding the null and alternative hypothesis.Explain why you made the decision that you did.

c.Interpret the meaning of the p-value in this case.

d.Based on the results of part b above, what is your decision as process manager?

3.An insurance company has the business objective of reducing the amount of time it takes to approve applications for life insurance.During the current month, you collect a random sample of 30 approved policies.The total processing time for these policies can be found in the Excel data file for this assignment under the tab Insurance.

In the past, the mean processing time was 45 days.Using the appropriate hypothesis test at the 0.05 level of significance (95% confidence), is there evidence that the mean processing time has changed from 45 days?

a.State the null and alternative hypothesis.

b.What is your conclusion?Justify your answer with the confidence interval and p-value.

c.What assumption about the population distribution is needed in order to conduct the test required in part a?

d.Do you feel the assumption stated in part b is valid?Justify your answer.

4.The population mean waiting time to check out of a supermarket has historically been 4 minutes.In an effort to reduce the waiting time, you, as store manager, conducted an experiment with infrared cameras that use body heat and in-store software to determine how many lanes should be opened.To test the effectiveness of this process, you selected a random sample of 100 customers and recorded their waiting time.For this sample, the mean waiting time to check out was 3.3 minutes, with a sample standard deviation of 2.0 minutes.

At the 0.05 level of significance (95% confidence level), is there evidence that the population mean waiting time to check out is less than 4 minutes?

a.State your null and alternative hypothesis

b.What is your conclusion based on this test?Justify your answer with the confidence interval and p-value.

c.Interpret the meaning of the p-value in this case.

d.Based on these results, what is your decision as store manager.

5.A cellphone provider wants their subscribers to upgrade to a new cellphone with improved features.Historically, the proportion of subscribers that typically upgrade every year is 25%. However, in order to increase sales, the provider will offer these new phones at a substantially reduced price if more than 25% of the subscribers will upgrade to the new phone.If at least 25% do not upgrade, they will lose money with this offer.Data is collected from a random sample of 500 subscribers, and 135 of these subscribers indicate they would upgrade at the reduced price if offered.

At the 0.05 level of significance (95% confidence), is there evidence that more than 25% of the subscribers would upgrade to the new cellphone at the reduced price?

a.State your null and alternative hypothesis.

b.What is your conclusion? Justify your answer the p-value and confidence interval.

c.Based on your conclusion in part b, what is your business decision?