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# Testing of hypothesis

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1. The manager of the Danvers-Hilton 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 weekend guest bills to test the manager's claim.
A. Which form of the hypotheses should be used to test the manager's claim? Explain.
H :µ &#8805; 600 H :µ &#8804; 600 H :µ = 600
° ° °

H :µ < 600 H µ > 600 H : µ &#8800; 600
ª ª ª
B. What conclusion is appropriate when H cannot be rejected?
°
C. What conclusion is appropriate when H can be rejected?
º

3. A production line operation is designed to fill cartons with laundry detergent to a mean weight of 32 ounces. A sample of carton 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 be shut down and adjusted to obtain proper filling.
A. Formulate the null and alternative hypotheses that will help in deciding whether to shut down and adjust the production line.

B. Comment on the conclusion and the decision when H cannot be rejected. H cannot be rejected. The o is suppose to below H °

C. Comment on the conclusion and the decision when H can be rejected.
°

7. Carpetland salespersons average \$8000 per week in sales. Steve Contois, the firm's vice president, proposes a compensation plan with new selling incentives. Steve hopes that the results of a trial selling period will enable him 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? What are the consequences of making this
Error?

C. What is the Type II error in this situation? What are the consequences of making this
Error?

9. Consider the following hypothesis test:
H :µ &#8805; 20
º
H :µ < 20
ª

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 a = .05, what is your conclusion?
d. What is the rejection rule using the critical value? What is your conclusion?

13. Consider the following hypothesis test:
H : µ &#8804; 50
º
H : µ > 50
ª

A sample of 60 is used and the population standard deviation is 8. Use the critical value approach to state your conclusion for each of the following sample results. Use a = 0.5
_
A. x = 52.5 _ is suppose to barely top of the x but I couldn't figure out how to
_ to do it.
B. x = 51
_
C. x = 51.8

17. The mean length of a work week for the population of workers was reported to be 39.2 hours. Suppose that we would like to take a current sample of workers to see whether the mean length of a work week has changed from the previously reported 39.2 hours.

A. State the hypotheses that will help us determine whether a change occurred in the mean length of a work week.

B. Suppose a current sample of 112 workers provided a sample mean of 38.5 hours. Use a population standard deviation = 4.8 hours. What is the p-value?

C. At a = .05 can the null hypothesis be rejected? What is your conclusion?

D. Repeat the preceding hypothesis test using the critical value approach.

19. In 2001, the US Department of Labor reported the average hourly earnings for US production workers to be \$14.32 per hour. A sample of wage rates for 75 production workers during 2003 is in the CD file named WageRate. Assume the population standard deviation = \$1.45, can we conclude that an increase occurred in the mean hourly earnings since 2001? Use a = .05.