stats

This final assignment for the course will count as both your score for exam 5 and homework #10. To receive credit for problems that involve equations you must show your work and explain which equations you used. You may use Excel where applicable. If so, describe which function from Excel was used. To complete the test you can create your own equations with the Equation Tool, or copy and paste the equations from the formula sheet at the end of the test and edit them with the correct numbers, or hand write your answers and then scan (picture) the document. (The more work you show, the more partial credit you can earn in the event a problem isn’t totally correct.) Then upload the document in the DROPBOX.

Section 9.1

1. (6pts) The manager of a Resort Hotel stated that the mean guest bill for a weekend is $600 or less. A member of the hotel’s accounting staff noticed that the total charges for guest bills have been increasing in recent months. The accountant will use a sample of future weekend guest bills to test the manager’s claim.

a) Circle the form of the hypotheses below that should be used to test the manager’s claim?

b) Comment on the conclusion when cannot be rejected.

c) Comment on the conclusion when can be rejected.

2. (6pts) The manager of an automobile dealership is considering a new bonus plan designed to increase sales volume. Currently, the mean sales volume is 14 automobiles per month. The manager wants to conduct a research study to see whether the new bonus plan increases sales volume. To collect data on the plan, a sample of sales personnel will be allowed to sell under the new bonus plan for a one-month period.

a) Develop the null and alternative hypotheses most appropriate for this situation.

b) Comment on the conclusion when cannot be rejected.

c) Comment on the conclusion when can be rejected.

3. (6pts) A production line operation is designed to fill cartons with laundry detergent to a mean weight of 32 ounces. A sample of cartons is periodically selected and weighed to determine whether underfilling or overfilling is occurring. If the sample data lead to a conclusion of underfilling or overfilling, the production line will shut down and be adjusted to obtain proper filling.

a) Develop the null and alternative hypotheses that will help in deciding whether to shut down and adjust the production line.

b) Comment on the conclusion when cannot be rejected.

c) Comment on the conclusion when can be rejected.

4. (6pts) Because of high production-changeover time and costs, a director of manufacturing must convince management that a proposed manufacturing method reduces costs before the new method can be implemented. The current production method operates with a mean cost of $220 per hour. A research study will measure the cost of the new method over a sample production period.

a) Develop the null and alternative hypotheses that will help in deciding whether to shut down and adjust the production line.

b) Comment on the conclusion when cannot be rejected.

c) Comment on the conclusion when can be rejected.

Section 9.2

5. (6pts) The label on a 3-quart container of orange juice states that the orange juice contains an average of 1 gram of fat or less. Answer the following questions for a hypothesis test that could be used to test the claim on the label.

a) Develop the appropriate null and alternative hypotheses.

b) What is the Type I error in this situation?

c) What is the Type II error in this situation?

6. (6pts) Carpetland salesperson average $8000 per week in sales. Sharon, the firm’s vice president, proposes a compensation plan with new selling incentives. Sharon hopes that the results of a trial selling period will enable her to conclude that the compensation plan increases the average sales per salesperson.

a) Develop the appropriate null and alternative hypotheses.

b) What is the Type I error in this situation?

c) What is the Type II error in this situation?

Section 9.3

7. (9pts) Consider the following hypothesis test:

A sample of 50 provided a sample mean of 19.4. The population standard deviation is 2.

a) Compute the value of the test statistic.

b) What is the p-value?

c) Using α = 0.05, what is your conclusion?

8. (9pts) Consider the following hypothesis test:

A sample of 40 provided a sample mean of 26.4. The population standard deviation is 6.

a) Compute the value of the test statistic.

b) What is the p-value?

c) Using α = 0.01, what is your conclusion?

9. (9pts) Consider the following hypothesis test:

A sample of 50 provided a sample mean of 14.5. The population standard deviation is 3.

a) Compute the value of the test statistic.

b) What is the p-value?

c) Using α = 0.05, what is your conclusion?

10. (9pts) Individuals filing federal income tax returns prior to March 31st received an average refund of $1056. Consider the population of “last-minute” filers who mail their tax return during the last five days of the income tax period.

a) A researcher suggest that a reason individuals wait until the last five days is that on average these individuals receive lower refunds than do early filers. Develop appropriate hypotheses such that rejection of will support the researcher’s contention.

b) For a sample of 400 individuals who filed a tax return last minute, the sample mean refund was $910. Based on prior experience, a population standard deviation of may be assumed. What is the p-value?

c) At α = 0.05, what is your conclusion?