Question: The null hypothesis is that the new process is as good or better than the old one. The Type I error is
a. to conclude that the new process is as good or better when it is not.
b. to conclude that the old process is better when it is.
c. to conclude that the old process is better when it is not.
d. to conclude that the new process is as good or better when it is.

2. The null hypothesis is that a process is producing no more than the maximum allowable rate of defective items. The Type II error is
a. to conclude that the process is producing too many defectives when it actually is not.
b. to conclude that the process is not producing too many defectives when it actually is.
c. to conclude that the process is not producing too many defectives when it is not.
d. to conclude that the process is producing too many defectives when it is.

3. Which of the answers in the above question imply neither a Type I nor a Type II error?
a. none of them
b. a) and b)
c. c) and d)
d. b) and c)

4. The Type II error is equivalent to rejecting the alternative hypothesis when it is true.
a. true
b. false

5. A significance level of 5% gives a lower probability of a Type I error than a significance level of 10%.
a. true
b. false


6. It is clear that no one should ever reject a null hypothesis that has a significance level of greater than 5%.
a. true
b. false

7. If r=-.999, we can say that X and Y are not highly correlated.
a. true
b. false

8. If the null hypothesis is false and the sample results cause the null hypothesis to not be rejected, a Type II error has been committed.
a. true
b. false

FOR THE NEXT FIVE QUESTIONS CONSIDER THAT THE MANAGER OF THE PEPPER ARENA WANTS TO DETERMINE IF THE AVERAGE AMOUNT SOLD PER PURCHASE DURING BASKETBALL GAMES IS MORE THAN THE $1.32 CLAIMED BY THE CONCESSIONAIRE. HE FEELS THAT THE CONCESSIONAIRE MAY BE UNDERSTATING PEPPER ARENA’S SHARE OF CONCESSION SALES. HE HAS A CONSULTANT RANDOMLY OBSERVE THE ACTIVITIES OF THE CONCESSIONAIRE. THE AVERAGE OF THE 75 PURCHASES OBSERVED WAS $1.46 WITH A STANDARD DEVIATION OF $0.32. DO THESE SAMPLE RESULTS SUPPORT THE MANAGER’S CONCERN? PERFORM THE HYPOTHESIS TEST USING ALPHA = .04, AND USE THE Z-DISTRIBUTION.

9. What is the appropriate alternate hypothesis for this hypothesis test?
a. mu does not equal 1.32
b. mu is less than 1.46
c. mu is not equal to 1.46
d. mu exceeds 1.32
e. mu is less than 1.32

10. What is the appropriate decision rule for the hypothesis test in the above problem? Reject the null hypothesis if
a. z-critical value exceeds 1.75.
b. z-critical value exceeds 2.05.
c. z-critical value is less than -2.05 or z-critical value exceeds 2.05.
d. z-critical value is less than -1.75.
e. z-critical value is less than -1.75 or z-critical value exceeds 1.75.

11. If choice (a) above were expressed as a p-value, then that the decision rule would be reject the null hypothesis if p
a. is less than 4 percent.
b. exceeds 4 percent.
c. is less than 2 percent.
d. exceeds 2 percent.

12. What is the calculated value of the z-statistic determined form the sample data?
a. -2.14
b. 3.79
c. 32.81
d. 2.14
e. -3.79

13. If the proper decision rule is reject if z-critical value exceeds 2.05, then the null hypothesis would be rejected if which of the following choices in the above problem were calculated?
a. a) or b)
b. c) or d)
c. b) or c) or d)
d. any of them

14. A statistician performs a hypothesis test but has no preconceived idea about at what value at she should reject the null hypothesis for this one-tailed test. If her calculated Z-statistic were 1.28, she could reject the null hypothesis at a minimum p-value of
a. 5-percent.
b. 10-percent.
c. 15-percent.
d. 90-percent.

15. Consider the above problem but in this instance she has 20 observations and a calculated t-statistic of 2.00. How many degrees of freedom should she use in evaluating the calculated statistic?
a. 19
b. 20
c. 30
d. 100

16. She can reject the null hypothesis based on the t-statistic at a minimum level of
a. .005 to .01
b. .01 to .025
c. .025 to .050
d. .050 to .10

A PROFESSOR GIVES THE SAME EXAM TO DIFFERENT SECTIONS OF A STATISTICS COURSE. THE FOLLOWING IS THE RELEVANT DATA:
CLASS I:
n=10
x-bar = 266.44
sigma squared = 2,467.8

CLASS II:
n=7
x-bar = 208.57
sigma squared = 1,755.10

ANSWER THE NEXT THREE QUESTIONS BASED ON THE DATA:

17. The professor decides to give do a hypothesis test to determine if Class I performs better than Class II. This will require a test of the difference between two means. Because of the test he is using and the small size of both classes, the populations should be __________ and the distributions __________.
a. independent // be binomial
b. dependent // be binomial
c. independent // be such that they can be approximated by the normal distribution
d. dependent // be skewed by the t-distribution

18. If the professor decides to test at the 5 percent significance level, he should reject the null hypothesis if
a. z-critical exceeds 1.645 and conclude that Class I is better than Class II.
b. z-critical exceeds 1.96 and conclude that Class I is better than Class II.
c. z-critical exceeds 1.645 and conclude that Class I is the same as Class II.
b. z-critical exceeds 1.96 and conclude that Class I is the same as Class II.

19. If the professor decides to test that Class I exceeds the performance of Class I by 10 points, then he is less likely to reject the null hypothesis.
a. true
b. false

20. ________ studied economics, and __________ has a PhD in history.
a. Tiger Woods // Newt Gingrich
b. Diana Ross // Donna Summer
c. Ronald Reagan // Mick Jagger
d. Tom Cruise // Denzel Washington


21. Calculate the test-statistic and decide whether to reject the null hypothesis based on the performance of the two classes discussed above. State what the conclusion is based on the statistical test (e.g. conclude the classes did equally well.)

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