01: The p-value is a probability that measures the support or lack of support for the
A) alternative hypothesis
B) null hypothesis
C) either the null or the alternative hypothesis
D) sample statistic
E). none of the above
02: In a t-test, which of the following does not need to be known in order to compute the p-value?
A) knowing whether the test is one-tail or two-tails
B) the value of the test statistic
C) the level of significance
D) the Degrees of Freedom
E) none of the above
03: As the test statistic becomes larger, the p-value
A) becomes smaller
B) becomes larger
C) becomes negative
D) stays the same because the sample size has not been changed
E) none of the above
04: The level of significance α is the
A) same as the p-value
B) 1 - β
C) maximum allowable probability of Type II error
D) maximum allowable probability of Type I error
E) none of the above
05: In hypotheses testing if the null hypothesis has been rejected when the alternative hypothesis is true, then
A) a Type I error has been committed
B) a Type II error has been committed
C) either a Type I or Type II error has been committed
D) the correct decision has been made
E) none of the above
06: In a one-tail, left-tail z-test, the test statistic is z = -2.01. The p-value is
A) 0.0179
B) 0.9778
C) 0.0222
D) 0.0174
E) none of the above
07: In a two-tail z-test, the test statistic is z = -2.5. The p-value for this test is
A) -1.25
B) 0.4938
C) 0.0062
D) 0.0124
E) none of the above
08: In a two-tail t-test, the test statistic t = -2.89 and the sample size is 30. The p-value is
A) 0.9928
B) 0.0019
C) 0.0072
D) 0.0036
E). None of the above
09. A soft drink filling machine, when in perfect adjustment, fills the bottles with 12 ounces of soft drink. If the machine overfills or under fills then it must be shut down and readjusted. To determine whether or not the machine is properly adjusted, the correct set of hypotheses is
A) H0: µ < 12 HA: µ ≥ 12
B) H0: µ = 12 HA: µ > 12
C) H0: µ ≠ 12 HA: µ = 12
D) H0: µ = 12 HA: µ ≠ 12
E) H0: µ = 12 HA: µ < 12
Use the following information to do the next four problems.
A random sample of 100 people was taken. In the sample 85% favored Candidate Green. We are interested in determining whether or not the proportion of the population in favor of Green is significantly more than 80%.
10. The correct set of hypotheses for this problem is
A) H0: p = 0.85 and HA: p > 0.85
B) H0: p > 0.80 and HA: p = 0.80
C) H0: p = 0.80 and HA: p > 0.80
D) H0: p = 0.80 and HA: p ≥ 0.80
E) H0: p ≠ 0.80 and HA: p > 0.80
11. Find the test statistic.
A) 0.80
B) 0.05
C) 1.25
D) 2.00
E) None of the above
12. Find the p-value.
A) 0.1071
B) 0.8929
C) 0.8944
D) 0.1056
E) none of the above
13. At the 5% level of significance, can we conclude that the proportion of the population in favor of Green
A) is significantly greater than 80%
B) is not significantly greater than 80%
C) is significantly greater than 85%
D) is not significantly greater than 85%
E) none of the above
Use the following information to do the next four problems.
The sales of a grocery store had an average of $8,000 per day. The store started an aggressive advertizing campaign in order to increase sales. To determine whether or not the advertizing campaign has been effective, i.e. the sales increased, a sample of 66 days was selected. For this sample the mean was $8,300 per day and the sample standard deviation $1,200.
14. The correct Alternative Hypothesis for this problem is
A) HA: > 8,000
B) HA: ≥ 8,000
C) HA: µ > 8,300
D) HA: µ ≥ 8,000
E) HA: none of the above
15. The value of the test statistic is
A) -2.03
B) 2.03
C) -2.00
D) 2.00
E) None of the above
16. The p-value is
A) 0.0248
B) 0.0228
C) 0.9752
D) 0.9768
E) 0.0232
17. At the 5% level of significance, can we conclude that the advertizing campaign
A) Increased sales?
B) Decreased sales?
C) Did not much affect sales?
D) Was not worth the cost?
E) None of the above
Use the following information to do the next four problems.
In October the campus bookstore asked a random sample of freshmen and seniors how much they had spent on textbooks that semester. The bookstore believes that the two groups spent the same amount. The results of the study are shown below.
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Freshmen
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Seniors
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= $280
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= 260
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= $47
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= $57
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= 80
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= 80
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18. To test the claim that the two groups spent the same amount the set of hypotheses is
A) and
B) and
C) and
D) and
E) and
19. Find the test statistic z.
A) 1.96
B) 1.645
C) 2.276
D) 2.42
E) 2.17
20. Find the p-value
A) 0.9922
B) 0.0156
C) 0.0078
D) 0.0187
E) None of the above
21. At the 5% level of significance we can conclude
A) That the two groups spent the same amounts.
B) That the two groups did not spent the same amounts.
C) The freshmen spent more.
D) The seniors spent more.
E) None of the above
Use the following to answer the next six questions:
A researcher wanted to determine if using an octane booster would increase gasoline mileage. A random sample of seven cars was selected; the cars were driven for two weeks without the booster and two weeks with the booster. Use the definitions of X1 and X2 as given in the table.
Consequently D = X1 - X2.
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X1 =mileage without booster
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X2 =mileage with booster
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21.2
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23.8
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25.4
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25.6
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20.9
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22.4
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27.6
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28.3
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22.8
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24.5
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27.3
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28.8
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23.4
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25.2
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22. State the Alternative Hypothesis
A)
B)
C)
D)
E) None of the above
23. Determine the mean of the differences
A) -1.67
B) 6.3
C) 1.67
D) -1.43
E) None of the above
24. Compute the standard deviation of the differences
A) 0.84
B) 0.78
C) 0.13
D) 0.11
E) None of the above
25. What critical value should be used at α = 0.05?
A) 1.895
B) -2.365
C) -1.943
D) -1.895
E) None of the above
26. Determine the test statistic
A) 4.85
B) 1.943
C) -3.96
D) -4.85.
E) None of the above
27. What is the p-value?
A) 0.0028.
B) 0.0014.
C) 0.0009
D) 0.0001
E) None of the above