Estadustica

Chapter 9
Hypothesis Testing

Learning Objectives

1. Learn how to formulate and test hypotheses about a population mean and/or a population proportion.

2. Understand the types of errors possible when conducting a hypothesis test.

3. Be able to determine the probability of making various errors in hypothesis tests.

4. Know how to compute and interpretp-values.

5. Be able to determine the size of a simple random sample necessary to keep the probability of hypothesis testing errors within acceptable limits.

6. Know the definition of the following terms:

null hypothesis one-tailed test
alternative hypothesis two-tailed test
type I error p-value
type II error operating characteristic curve
critical valuepower curve
level of significance

Solutions:

1. a. H0: μ ≤ 600 Manager’s claim.

Ha: μ > 600

b. We are not able to conclude that the manager’s claim is wrong.

c. The manager’s claim can be rejected. We can conclude that μ > 400.

2. a. H0: μ ≤ 14

Ha: μ > 14 Research hypothesis

b. There is no statistical evidence that the newbonus plan increases sales volume.

c. The research hypothesis that μ > 14 is supported. We can conclude that the new bonus plan increases the mean sales volume.

3. a. H0: μ = 32 Specified filling weight

Ha: μ ≠ 32 Overfilling or underfilling exists

b. There is no evidence that the production line is not operating properly. Allow the productionprocess to continue.

c. Conclude μ ≠ 32 and that overfilling or underfilling exists. Shut down and adjust the production line.

4. a. H0: μ ≥ 220

Ha: μ < 220 Research hypothesis to see if mean cost is less than $220.

b. We are unable to conclude that the new method reduces costs.

c. Conclude μ < 220. Consider implementing the new methodbased on the conclusion that it lowers the mean cost per hour.

5. a. The Type I error is rejecting H0 when it is true. In this case, this error occurs if the researcher concludes that the mean newspaper-reading time for individuals in management positions is greater than the national average of 8.6 minutes when in fact it is not.

b. The Type II error is accepting H0 when it isfalse. In this case, this error occurs if the researcher concludes that the mean newspaper-reading time for individuals in management positions is less than or equal to the national average of 8.6 minutes when in fact it is greater than 8.6 minutes.

6. a. H0: μ ≤ 1 The label claim or assumption.

Ha: μ > 1

b. Claiming μ > 1 when it is not. This is the error ofrejecting the product’s claim when the claim is true.

c. Concluding μ ≤ 1 when it is not. In this case, we miss the fact that the product is not meeting its label specification.
7. a. H0: μ ≤ 8000

Ha: μ > 8000 Research hypothesis to see if the plan increases average sales.

b. Claiming μ > 8000 when the plan does not increase sales. A mistakecould be implementing the plan when it does not help.

c. Concluding μ ≤ 8000 when the plan really would increase sales. This could lead to not implementing a plan that would increase sales.

8. a. H0: μ ≥ 220

Ha: μ < 220

b. Claiming μ < 220 when the new method does not lower costs. A mistake could be implementing the method when it does not help.c. Concluding μ ≥ 220 when the method really would lower costs. This could lead to not implementing a method that would lower costs.

9. a. z = -1.645

Reject H0 if z < -1.645

b. [pic]

Reject H0; conclude Ha is true.

10. a. z = 2.05

Reject H0 if z > 2.05

b. [pic]

c. Area from z = 0 to z = 1.36 is .4131...