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Administrative Studies

ADMS 2320

Marwan Hassan

Winter

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CHAPTER 11
INTRODUCTION TO HYPOTHESIS TESTING
MULTIPLE CHOICE QUESTIONS
In the following multiple-choice questions, please circle the correct answer.
1. In order to determine the p-value, which of the following is not needed?
a. The level of significance
b. Whether the test is one or two tail
c. The value of the test statistic
d. All of the above are needed
ANSWER: a
2. In testing the hypotheses
H 0 μ =50
50
H 1μ≠
the following information is known: n = 64, x = 53.5, and σ = 10. The
standardized test statistic equals:
a. 1.96
b. –2.8
c. 2.8
d. –1.96
ANSWER: c
3. If a hypothesis is not rejected at the 0.10 level of significance, it:
a. must be rejected at the 0.05 level
b. may be rejected at the 0.05 level
c. will not be rejected at the 0.05 level
d. must be rejected at the 0.025 level
ANSWER: c
175 176 Chapter Eleven
4. In testing the hypothesis
H 0 μ = 75
μ
H 1 < 75
if the value of the test statistic equals –2.42, then the p-value is:
a. 0.5078
b. 2.420
c. 0.9922
d. 0.0078
ANSWER: d
5. For a two-tail test, the null hypothesis will be rejected at the 0.05 level of
significance if the value of the standardized test statistic is:
a. smaller 1.96
b. greater than –1.96
c. smaller than –1.96
d. smaller than 1.645
ANSWER: c
6. In testing the hypothesis
H 0 μ = 800
H :μ≠ 800
1
if the value of the test statistic equals 1.75, then the p-value is:
a. 0.0401
b. 0.0802
c. 0.4599
d. 0.9198
ANSWER: b
7. If a hypothesis is rejected at the 0.025 level of significance, it:
a. must be rejected at any level
b. must be rejected at the 0.01 level
c. must not be rejected at the 0.01 level
d. may be rejected or not rejected at the 0.01 level
ANSWER: d
8. The power of a test is the probability of making:
a. a correct decision when the null hypothesis is false
b. a correct decision when the null hypothesis is true
c. incorrect decision when the null hypothesis is false
d. incorrect decision when the null hypothesis is true
ANSWER: a Introduction to Hypothesis Testin177
9. A Type II error is committed if we make:
a. a correct decision when the null hypothesis is false
b. correct decision when the null hypothesis is true
c. incorrect decision when the null hypothesis is false
d. incorrect decision when the null hypothesis is true
ANSWER: c
10. A Type I error is committed if we make:
a. a correct decision when the null hypothesis is false
b. correct decision when the null hypothesis is true
c. incorrect decision when the null hypothesis is false
d. incorrect decision when the null hypothesis is true
ANSWER: d
11. Which of the following p-values will lead us to reject the null hypothesis if the
level of significance equals 0.05?
a. 0.15
b. 0.10
c. 0.05
d. 0.025
ANSWER: d
12. A professor of statistics refutes the claim that the average student spends 3
hours studying for the midterm exam. Which hypothesis is used to test the
claim?
a. H 0μ≠ 3
H : μ > 3
1
b. H 0 μ = 3
H : μ ≠ 3
1
c. H :μ≠ 3
0
H : μ = 3
1
d. H 0 μ = 3
H : μ < 3
1
ANSWER: b
13. Suppose that we reject a null hypothesis at the 0.05 level of significance. Then
for which of the followingα -values do we also reject the null hypothesis?
a. 0.06
b. 0.04
c. 0.03
d. 0.02
ANSWER: a 178 Chapter Eleven
14. The critical values α or zα / 2re the boundary values for the:
a. rejection region(s)
b. level of significance
c. power of the test
d. type II error
ANSWER: a
15. Using the confidence interval when conducting a two-tail test for the population
μ μ
mean we do not reject the null hypothesis if the hypothesized value for :
a. is to the left of the lower confidence limit (LCL)
b. is to the right of the upper confidence limit (UCL)
c. falls between the LCL and UCL
d. falls in the rejection region
ANSWER: c
16. In a two-tail test for the population mean, if the null hypothesis is rejected when
the alternative hypothesis is true,
a. a Type I error is committed
b. a Type II error is committed
c. a correct decision is made
d. a one-tail test should be used instead of a two-tail test
ANSWER: c
17. In a one-tail test for the population mean, if the null hypothesis is not rejected
when the alternative hypothesis is true,
a. a Type I error is committed
b. a Type II error is committed
c. a two-tail test should be used instead of a one-tail test
d. a two-tail test should be used instead of a one-tail test
ANSWER: b
18. In hypothesis testing, whatever we are investigating or researching is specified
as:
a. the null hypothesis
b. the alternative hypothesis
c. either the null or alternative
d. the p-value
ANSWER: b
19. In a two-tail test for the population mean, the null hypothesis will be rejected at
α level of significance if the value of the standardized test statistic z is such
that:
a. z > z α
b. z < -z
α
c. -z α < z < zα
d. |z| > z
α / 2
ANSWER: d
20. In testing the hypothesis Introduction to Hypothesis Testing 179
H 0 μ = 100
H 1 μ >100
the p-value is found to be 0.0738, and the sample mean is 105. Which of
the following statements is true?
a. The probability of observing a sample mean at least as large as 105 from a
population whose mean is 100 is 0.0738.
b. The probability of observing a sample mean smaller than 105 from a
population whose mean is 100 is 0.0738
c. The probability that the population mean is larger than 100 is 0.0738
d. None of the above statements is correct
ANSWER: a
21. Statisticians can translate p-values into several descriptive terms. Which of the
following statements is correct?
a. If p-value < 0.01, there is overwhelming evidence to infer that the alternative
hypothesis is true
b. If 0.01 < p-value < 0.05, there is strong evidence to infer that the alternative
hypothesis is true
c. If 0.05 < p-value < 0.10, there is weak evidence to infer that the alternative
hypothesis is true
d. All of the above statements are correct
ANSWER: d
22. A spouse stated that the average amount of money spent on Christmas gifts for
immediate family members is above $1200. The correct set of hypotheses is:
a. H 0 μ = 200
H : μ <1200
1
b. H 0 μ > 1200
H : μ = 1200
1
c. H 0 μ = 1200
H 1 μ >1200
d. H0: μ < 1200
H 1 μ = 1200
ANSWER: c
23. The confidence interval approach can be employed to conduct tests of
hypotheses. Which of the following statements is false?
a. The confidence interval approach is equivalent to the rejection region
approach
b. The confidence interval approach has the disadvantage of complexity
c. One-sided confidence intervals can be used when conducting a one-tail test
d. The confidence interval approach does not yield a p-value
ANSWER: b
24. Whenever the null hypothesis is not rejected, the alternative hypothesis:
a. is rejected 180 Chapter Eleven
b. is not rejected
c. must be modified
d. is true
ANSWER: a
25. The probability of a Type I error is denoted by:
a. β
β
b. 1-
c. α
d. 1-α
ANSWER: c
26. A Type I error occurs when we:
a. reject a false null hypothesis
b. reject a true null hypothesis
c. don’t reject a false null hypothesis
d. don’t reject a true null hypothesis
ANSWER: b
27. A Type II error is defined as:
a. rejecting a true null hypothesis
b. rejecting a false null hypothesis
c. not rejecting a true null hypothesis
d. not rejecting a false null hypothesis
ANSWER: d
28. The probability of a Type II error is denoted by:
a. α
b. β
c. 1-α
e. 1-β
ANSWER: b
29. The power of a test is the probability that it will lead us to :
a. reject the null hypothesis when it is true
b. reject the null hypothesis when it is false
c. fail to reject the null hypothesis when it is true
d. fail to reject the null hypothesis when it is false
ANSWER: b
30. The power of a test is denoted by:
a. α
b. β
c. 1-α
β
d. 1-
ANSWER: d
31. If we reject the null hypothesis, we conclude that :
a. there is enough statistical evidence to infer that the alternative hypothesis is
true Introduction to Hypothesis Testi181
b. there is not enough statistical evidence to infer that the alternative
hypothesis is true
c. there is enough statistical evidence to infer that the null hypothesis is true
d. the test is statistically insignificant at whatever level of significance the test
was conducted at
ANSWER: a
32. In a given hypothesis test, the null hypothesis can be rejected at the .10 and .05
level of significance, but cannot be rejected at the .01 level. The most accurate
statement about the p-value for this test is:
a. p-value = 0.01
b. p-value = 0.10
c. 0.01 < p-value < 0.05
d. 0.05 < p-value < 0.10
ANSWER: c
33. In a criminal trial, a Type I error is made when:
a. a guilty defendant is acquitted
b. an innocent person is convicted
c. a guilty defendant is convicted
d. an innocent person is acquitted
ANSWER: b
34. If we do not reject the null hypothesis, we conclude that:
a. there is enough statistical evidence to infer that the alternative hypothesis is
true
b. there is not enough statistical evidence to infer that the alternative
hypothesis is true
c. there is enough statistical evidence to infer that the null hypothesis is true
d. the test is statistically insignificant at whatever level of significance the test
was conducted at
ANSWER: b
35. Which of the following statements is (are) not true?
a. The probability of making a Type II error increases as the probability of
making a Type I error decreases
b. The probability of making a Type II error and the level of significance are the
same
c. The power of the test decreases as the level of significance decreases
d. All of the above statements are not true
ANSWER: b
36. In a criminal trial, a Type II error is made when:
a. a guilty defendant is acquitted
b. an innocent person is convicted
c. a guilty defendant is convicted
d. an innocent person is acquitted
ANSWER: a 182 Chapter Eleven
37. In a one-tail test, the p-value is found to be equal to 0.068. If the test had been
two-tail, the p-value would have been:
a. 0.932
b. 0.466
c. 0.034
d. 0.136
ANSWER: d
38. If the value of the sample meanx is close enough to the hypothesized value of
μ
the population mean , then:
a. the hypothesized value is definitely true
b. the hypothesized value is definitely false
c. we reject the null hypothesis
d. we don’t reject the null hypothesis
ANSWER: d
39. We cannot commit a Type I error when the:
a. null hypothesis is true
b. level of significance is 0.10
c. null hypothesis is false
d. test is a two-tail test
ANSWER: c
40. For a given level of significance, if the sample size increases, the probability of a
Type II error will:
a. remain the same
b. increase
c. decrease
d. be equal to 1.0 regardless of
ANSWER: c
41. The p-value of a test is the:
a. smallestα at which the null hypothesis can be rejected
b. largestα at which the null hypothesis can be rejected
c. smallestα at which the null hypothesis cannot be rejected
α
d. largest at which the null hypothesis cannot be rejected
ANSWER: a
42. The rejection region for testing
H 0 μ = 100
H :μ≠ 100
1
at the 0.05 level of significance is:
a. |z| < 0.95
b. |z| > 1.96
c. z > 1.65
d. z < 2.33
ANSWER: b
43. The rejection region for testing Introduction to Hypothesis Test183
H : μ =
0 80
H 1 μ < 80
at the 0.10 level of significance is:
a. z > 1.96
b. z < 0.90
c. z > -1.65
d. z < -1.28
ANSWER: d
44. The level of significance can be:
a. any value between –1.04 and 1.04
b. any positive value
c. any value smaller than 1.645
d. None of the above answers is correct
ANSWER: d
45. The p-value criterion for hypothesis testing is to reject the null hypothesis if:
a. p-value =α
b. p-value α
d. -α < p-value

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