: 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
Stat 200-Quiz 3 Dr. T
Multiple-choice: Choose only ONE answer in each question.
Submit only the answers. There are 27 problems for 80 points total.
01: 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
02: 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
03: In a hypotheses testing procedure, α is the
A) Confidence
level
B) same as the p-value
C) 1 – β
D) maximum allowable probability of
Type II error
E) maximum allowable probability of
Type I error
04: 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
05: The average life expectancy of a certain
brand of tire has been 40,000 miles. Because of a new manufacturing process
introduced it is believed that the life expectancy has increased. To test the validity of this the correct set of
hypotheses is
A) H0: µ < 40,000 HA: µ ≥ 40,000
B) H0: µ = 40,000 HA: µ ≥ 40,000
C) H0: µ > 40,000 HA: µ ≤ 40,000
D) H0: µ = 40,000 HA: µ < 40,000
E) H0: µ = 40,000 HA: µ > 40,000
06: What kind of Alternative Hypothesis is used in the figure below?
A. HA: µ = µ0
B. HA: µ ≠ µ0 C. HA: µ > µ0D. HA: µ < µ0
E. none of the above
07. Which type of Alternative Hypothesis is used in the figure below?
A. HA: µ = µ0
B. HA: µ ≠ µ0
C. HA: µ > µ0 D. HA: µ < µ0
E. none of the above
08: 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%.
09: 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
10: Find the test statistic.
A) 0.80
B) -1.25
C) 1.25
D) 2.00
E) none of the above
11: Find the p-value.
A) 0.1071
B) 0.8929
C) 0.8944
D) 0.1056
E) none of the above
12: 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 advertising campaign in order to increase sales. To determine whether or not the advertising 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 standard deviation $1,200.
13: 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
14: The value of the test statistic is
A) -2.03
B) 2.03.
C) -2.00
D) 2.00
E) none of the above
15: The p-value is
A) 0.0248
B) 0.0228
C) 0.9752
D) 0.9768
E) 0.0232
16: At the 5% level of significance, we conclude that the advertising 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 five 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.
| Freshmen | Seniors |
| = $280 | = 260 |
| = $47 | = $57 |
| = 80 | = 80 |
17. Which of the following statements is true?
A) This is a two-tail test of two dependent samples.
B) This is a two-tail t-test of two independent samples.
C) This is a two-tail z-test of two independent samples.
D) This is a test of matched pairs.
E) None of the above
18. To test the claim that the two groups spent the same amount the set of hypotheses is
A),
B),
C),
D),
E),
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.
Take d= X1 – X2 = Without booster – With booster.
| X1 =mileage without booster | X2 =mileage with booster | d= X1– X2 | d2 =( X1– X2)2 | |
| 1 | 21.2 | 23.8 | ||
| 2 | 25.4 | 25.6 | ||
| 3 | 20.9 | 22.4 | ||
| 4 | 27.6 | 28.3 | ||
| 5 | 22.8 | 24.5 | ||
| 6 | 27.3 | 28.8 | ||
| 7 | 23.4 | 25.2 | ||
| Σd = | Σd2 = | |||
| d‾ = |
You should fill in the table.
22. State the
Alternative Hypothesis
A)
B)
C)
D)
E) None of the above
23. Compute 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. Determine the test statistic
A) 4.85
B) 1.943
C) -3.96
D) -4.85.
E) None
of the above
26. What is the p-value?
A) 0.0028.
B) 0.0014.
C) 0.0009
D) 0.0001
E) None
of the above
27. At α = 0.05 the
correct decision and conclusion are
A) Reject H0, Booster does not increase mileage
B) Reject H0, Booster increases mileage C) Fail to reject H0, Booster does not increase mileage
D) Fail to reject H0, Booster increases mileage
E) None of the above
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