1. Which of the following would be an appropriate null hypothesis?

a) The mean of a population is equal to 55.

b) The mean of a sample is equal to 55.

c) The mean of a population is greater than 55.

d) Only (a) and (c) are true.

2. Which of the following would be an appropriate null hypothesis?

a) The population proportion is less than 0.65.

b) The sample proportion is less than 0.65.

c) The population proportion is no less than 0.65.

d) The sample proportion is no less than 0.65.

3. Which of the following would be an appropriate alternative hypothesis?

a) The mean of a population is equal to 55.

b) The mean of a sample is equal to 55.

c) The mean of a population is greater than 55.

d) The mean of a sample is greater than 55.

4. Which of the following would be an appropriate alternative hypothesis?

a) The population proportion is less than 0.65.

b) The sample proportion is less than 0.65.

c) The population proportion is no less than 0.65.

d) The sample proportion is no less than 0.65

5. A Type Ⅱ error is committed when

a) we reject a null hypothesis that is true.

b) we don’t reject a null hypothesis that is true.

c) we reject a null hypothesis that is false.

d) we don’t reject a null hypothesis that is false.

6. A Type Ⅰ is committed when

a) we reject a null hypothesis that is true.

b) we don’t reject a null hypothesis that is true.

c) we reject a null hypothesis that is false.

d) we don’t reject a null hypothesis that is false、

7. The power of a test is measured by its capability of

a) rejecting a null hypothesis that is true.

b) not rejecting a null hypothesis that is true.

c) rejecting a null hypothesis is false.

d) not rejecting a null hypothesis that is false.

8. If we are performing a two-tailed test of whether =100, the probabillity of

detecting a shift of the mean to 105 will be () the probability of detecting a shift of the

mean to 110.

a) less than

b) greater than

c) equal to

d) not comparable to

9.If an economist wishes to determine whether there is evidence that average family income in a community exceeds $25,000

a) either a one-tailed or two0tailed test could be used with equivalent results

b) a one-tailed test should be utilized

c) a two-tailed test should be utilized

d) none of the above.

10. If an economist wishes to determine whether there is evidence that average family income in a community equals $25,000

a) either a one-tailed or two0tailed test could be used with equivalent results

b) a one-tailed test should be utilized

c) a two-tailed test should be utilized

d) none of the above.

11. If the P-value is less than α in a two-tailed test,

a) the null hypothesis should not be rejected

b) the null hypothesis should be rejected

c) a one-tailed test should be used

d) no conclusion should be reached.

12. If a test of hypothesis has a Type Ⅰerror probability (α) of 0.01, we mean

a) if the null hypothesis is true, we don't reject it 1% of the time.

b) if the null hypothesis is true, we reject it 1% of the time.

c) if the null hypothesis is false, we don't reject it 1% of the time.

d) if the null hypothesis is false, we reject it 1% of the time.

13. If the Type Ⅰerror (α) for a given test is to be decreased, then for a fixed sample size n

a) the Type Ⅱ(β)will also decrease.

b) the Type Ⅱ(β)will increase.

c) the power of the test will increase.

d) a one-tailed must be utilized.

14. We have created a 95% confidence interval for μ with the result (10,15). What decision will we make if we test H。: μ=16 versus H1 : μ≠16 at α=0.10?

a) Reject H。in favor of H1.

b) Accept H。in favor of H1.

c) Fail to reject H。in favor of H1.

d) We cannot tell what our decision will be from the information given.

15. Suppose we want to test H。: μ≥30 versus H1:< 30. Which of the following possible sample results based on a sample of size 36 gives the strongest evidence to reject H。in favor of H1?

a) X =28, s=6

b) X=27,s=4

c) X=32,s=2

d) X=26,s=9

16. The marketing manager for an automobile manufacturer is interested in determined the proportion of new car owners who would have purchased a passenger-side inflatable air bag if it had been available for an additional cost of $300.The manager believes from previous information that the proportion is 0.30. Suppose that a survey of 200 new compact car owners is selected and 79 indicate that they would have purchased the inflatable air bag. If you were to conduct a test to determine whether there is evidence that the proportion is different from 0.30, which test would you use?

a)Z- test of a population mean

b) Z-test of a population proportion

c)T test of population mean

d) T test of a population proportion

17. The marketing manager for an automobile manufacturer is interested in determined the proportion of new car owners who would have purchased a passenger-side inflatable air bag if it had been available for an additional cost of $300.The manager believes from previous information that the proportion is 0.30. Suppose that a survey of 200 new compact car owners is selected and 79 indicate that they would have purchased the inflatable air bag. If you were to conduct a test to determine whether there is evidence that the proportion is different from 0.30 and decided not reject the null hypothesis, what conclusion could you draw?

a. There is sufficient evidence that the proportion is 0.30.

b. There is not sufficient evidence that the proportion is 0.30.

c. There is not sufficient evidence that the proportion is 0.30.

d. There is not sufficient evidence that the proportion is not 0.30.

18. Setup hypothesis H0

a) Experience has shown that the number of matches in boxes follows a normal distribution. A manufacturer claims that the average number of matches in its boxes is 50 (S388)

b) A tax driver claims to take an average of $12.00 on each fare, but the Taxation Office believes that the average is higher than that. (S390)

19. A normal distribution has μ=100 and σ=40. A random sample of size 25 is selected and found to have a mean of 90. The value of the z-test static for this mean is :

a) 0.25 b) -0.25  c) 8  

b) d) -1.25 e) none of the above (S400)

20. A question involves testing whether international soccer players are any different in height from others in the population. A type II error in a two tailed test for this problem would conclude that:

a) Soccer players are taller than others when they are really not

b) Soccer players are shorter than others when they are really not

c) Soccer players are the same height as others when they are really not

d) Soccer players are not the same height as others when they really are

e) None of the above (S400)

21. If you use a 0.05 level of significance in a (two tail) hypothesis test, what will you decide if the computed value of the test statistic Z is +2.21? ( 9.20 Manager P341)\

22. Suppose that in a two tail hypothesis test, you compute the value of the test statistic Z as +2.00 . what is the p-value? ( 9.24 Manager P341)

23. The personnel department of a company has been surveying employees and asking them how long it takes for them to travel from home to work each morning. It found that the distribution of times was skewed to the right with a mean of 21.6 minutes and a standard deviation of 7.2 minutes. A random sample of 25 employees in the accounts section took an average of 24.1 minutes to travel to work. Are these employees different from other employees in their travel time? (S386)

24. The number of newspapers sold each Friday in a news agency follows a normal distribution with μ=120 papers and σ=15 papers. On the Friday before a Federal election, the newsagency sold 130 papers. Is this significant increase in the number of papers sold? Use a one-side test at α=0.05 and draw appropriate conclusions. (S12.1 S402)

25.  The number of errors on the pages of a statistics textbook follows a normal distribution with a mean of 5.2 errors. In a chapter of 8 pages, the number of errors found on the pages was:  3 4 6 2 0 4 7 4

Does this chapter contain an unusual number of errors? Test at α=0.05.

26. A well known bank stores enough money during the weekends to satisfy its customers needs. The expected average withdrawal during the weekend is $550. When they looked at a sample of the last 36 weekend transactions, they found the average withdrawal to be $600 with a standard deviation of $70. At α=0.01, is there evidence that the mean withdrawal has increased during weekends?

 

27. The quality control manager wants to test whether the mean lifetime of batteries is 180 hours at the 5% level of significance. He picked a sample of 100 batteries and calculated the sample mean to be 195 hours. It is assumed that the lifetime of bulbs follows a normal distribution with a standard deviation of 20 hours.