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BU1007 Study Guide - Quiz Guide: Type I And Type Ii Errors, Null Hypothesis, Statistical Hypothesis Testing

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yellowpug748
15 May 2018
School
James Cook University
Department
BU
Course
BU1007
Professor
Dr Diane Jarvis

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CHAPTER 9—HYPOTHESIS TESTS
MULTIPLE CHOICE
1. The sum of the values of and
a.
always add up to 1.0
b.
always add up to 0.5
c.
is the probability of Type II error
d.
None of these alternatives is correct.
ANS: D PTS: 1 TOP: Hypothesis Tests
2. What type of error occurs if you fail to reject H0 when, in fact, it is not true?
a.
Type II
b.
Type I
c.
either Type I or Type II, depending on the level of significance
d.
either Type I or Type II, depending on whether the test is one tail or two tail
ANS: A PTS: 1 TOP: Hypothesis Tests
3. An assumption made about the value of a population parameter is called a
a.
hypothesis
b.
conclusion
c.
confidence
d.
significance
ANS: A PTS: 1 TOP: Hypothesis Tests
4. The probability of committing a Type I error when the null hypothesis is true is
a.
the confidence level
b.
c.
greater than 1
d.
the Level of Significance
ANS: D PTS: 1 TOP: Hypothesis Tests
5. In hypothesis testing,
a.
the smaller the Type I error, the smaller the Type II error will be
b.
the smaller the Type I error, the larger the Type II error will be
c.
Type II error will not be effected by Type I error
d.
the sum of Type I and Ttype II errors must equal to 1
ANS: B PTS: 1 TOP: Hypothesis Tests
6. In hypothesis testing, the tentative assumption about the population parameter is
a.
the alternative hypothesis
b.
the null hypothesis
c.
either the null or the alternative
d.
None of these alternatives is correct.
ANS: B PTS: 1 TOP: Hypothesis Tests
7. For a lower tail test, the p-value is the probability of obtaining a value for the test statistic
a.
at least as small as that provided by the sample
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b.
at least as large as that provided by the sample
c.
at least as small as that provided by the population
d.
at least as large as that provided by the population.
ANS: A PTS: 1 TOP: Hypothesis Tests
8. The p-value is a probability that measures the support (or lack of support) for the
a.
null hypothesis
b.
alternative hypothesis
c.
either the null or the alternative hypothesis
d.
sample statistic
ANS: A PTS: 1 TOP: Hypothesis Tests
9. The p-value
a.
is the same as the Z statistic
b.
measures the number of standard deviations from the mean
c.
is a distance
d.
is a probability
ANS: D PTS: 1 TOP: Hypothesis Tests
10. For a two-tail test, the p-value is the probability of obtaining a value for the test statistic as
a.
likely as that provided by the sample
b.
unlikely as that provided by the sample
c.
likely as that provided by the population
d.
unlikely as that provided by the population
ANS: B PTS: 1 TOP: Hypothesis Tests
11. In hypothesis testing if the null hypothesis is rejected,
a.
no conclusions can be drawn from the test
b.
the alternative hypothesis is true
c.
the data must have been accumulated incorrectly
d.
the sample size has been too small
ANS: B PTS: 1 TOP: Hypothesis Tests
12. The level of significance is the
a.
maximum allowable probability of Type II error
b.
maximum allowable probability of Type I error
c.
same as the confidence coefficient
d.
same as the p-value
ANS: B PTS: 1 TOP: Hypothesis Tests
13. The power curve provides the probability of
a.
correctly accepting the null hypothesis
b.
incorrectly accepting the null hypothesis
c.
correctly rejecting the alternative hypothesis
d.
correctly rejecting the null hypothesis
ANS: D PTS: 1 TOP: Hypothesis Tests
14. A Type II error is committed when
a.
a true alternative hypothesis is mistakenly rejected
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b.
a true null hypothesis is mistakenly rejected
c.
the sample size has been too small
d.
not enough information has been available
ANS: A PTS: 1 TOP: Hypothesis Tests
15. The error of rejecting a true null hypothesis is
a.
a Type I error
b.
a Type II error
c.
is the same as
d.
committed when not enough information is available
ANS: A PTS: 1 TOP: Hypothesis Tests
16. The level of significance in hypothesis testing is the probability of
a.
accepting a true null hypothesis
b.
accepting a false null hypothesis
c.
rejecting a true null hypothesis
d.
None of these alternatives is correct.
ANS: C PTS: 1 TOP: Hypothesis Tests
17. The level of significance
a.
can be any positive value
b.
can be any value
c.
is (1 - confidence level)
d.
can be any value between -1.96 to 1.96
ANS: C PTS: 1 TOP: Hypothesis Tests
18. In hypothesis testing if the null hypothesis has been rejected when the alternative hypothesis has been
true,
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
ANS: D PTS: 1 TOP: Hypothesis Tests
19. The probability of making a Type I error is denoted by
a.
b.
c.
1 -
d.
1 -
ANS: A PTS: 1 TOP: Hypothesis Tests
20. The probability of making a Type II error is denoted by
a.
b.
c.
1 -
d.
1 -
ANS: B PTS: 1 TOP: Hypothesis Tests
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Document Summary

Multiple choice: the sum of the values of and is the probability of type ii error, always add up to 1. 0, always add up to 0. 5, none of these alternatives is correct. Pts: 1: an assumption made about the value of a population parameter is called a, hypothesis, conclusion, confidence, significance. Top: hypothesis tests: the probability of committing a type i error when the null hypothesis is true is the confidence level the level of significance, greater than 1. Ans: b the sum of type i and ttype ii errors must equal to 1. Pts: 1: in hypothesis testing, the tentative assumption about the population parameter is the alternative hypothesis the null hypothesis, either the null or the alternative, none of these alternatives is correct. Top: hypothesis tests: the p-value is a probability that measures the support (or lack of support) for the, null hypothesis, alternative hypothesis, either the null or the alternative hypothesis, sample statistic.

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Related Questions

1 Which of the following statements about Type I and Type II errors is correct
a Type I: Reject a true alternative hypothesis. Type II: Do not reject a false alternative.
b Type I: Reject a true null hypothesis. Type II: Do not reject a false null hypothesis.
c Type I: Reject a false null hypothesis. Type II: Reject a true null hypothesis.
d Type I: Do not reject a false null hypothesis. Type II: Reject a true null hypothesis.
2 You are reading a report that contains a hypothesis test you are interested in. The writer of the report writes that the p-value for the test you are interested in is 0.0749, but does not tell you the value of the test statistic. From this information you can:
a Not reject the hypothesis at a Probability of Type I error = .05, but reject the hypothesis at a Probability of Type I error = 0.10
b Reject the hypothesis at a Probability of Type I error = .05, and reject at a Probability of Type I error = 0.10
c Not reject the hypothesis at a Probability of Type I error = 0.05, and not reject at a Probability of Type I error = 0.10
d Reject the hypothesis at a Probability of Type I error = .05, but not reject at a Probability of Type I error = 0.10
3 The random sample below is obtained to test the following hypothesis about the population mean.
H?: ? ? 1500
H?: ? > 1500
620 1711 366 2528 2678 1661 442 725 1938
409 330 2480 542 369 2124 549 2074 1665
1873 873 2143 2061 1177 2509 1264 2397 1523
1837 1958 1041 1639 2199 2232 387 2270 2136
1111 1883 2612 2230 1597 1726 694 1990 1354
2090 909 2128 1608 747 1121 2220 2390 2347
1041 316 655 632 2064 1901 532 552 846
2704 1410 2165 1065 937 1452 2539 410 656
1169 527 809 2364 2350 2210 1459 2391 856
2711 1985 2382 2289 1927 518 2177 437 1151
2018 1580 607 2715 2188 1691 1394 2610 1186
695 2428 2246 858 2036 1681 2449 1578 1971
1846 1729 2389 1737 1913 1863 2072 2593 2287
2220 2230 551 458 2626 2731 488 2551 1736
1373 307 1803 2647 2679 1508 1468 1443 516
1002 2116 2616 817 2522 460 1879 1999 1837
The level of significance of the test is ? = 0.05. Compute the relevant test statistic.
This is a(n) _______ (two-tail, upper-tail, lower-tail) test. The test statistic is TS = _______.
a Two-tail test TS = 1.81
Do not reject H?: ? ? 1500. Conclude that the population mean is not greater than 1500.
b Upper tail test. TS = 1.52
Do not reject H?: ? ? 1500. Conclude that the population mean is not greater than 1500.
c Upper tail test. TS = 1.81
Reject H?: ? ? 1500. Conclude that the population mean is greater than 1500.
d Lower tail test. TS = 1.98
Do not reject H?: ? ? 1500. Conclude that the population mean is no greater than 1500.
4 Consider the following hypothesis test.
H?: ? ? 30
H?: ? > 30
A random sample of n = 15 yielded the following observations
51 38 26 16 28
57 20 33 35 23
21 47 56 54 36
Use ? = 0.05
TS = ______ CV = ______ State the decision rule.
a 1.68 1.761 Do not reject H?. Conclude the mean is not greater than 30.
b 1.68 1.64 Reject H?. Conclude the mean is greater than 30.
c 1.847 2.145 Do not reject H?. Conclude the mean is not less than 30.
d 1.847 1.761 Reject H?. Conclude the mean is less than 30.
5 In a recent study, a major fast food restaurant had a mean service time of 165 seconds. The company embarks on a quality improvement effort to reduce the service time and has developed improvements to the service process. The new process will be tested in a sample of stores. The new process will be adopted in all of its stores, if it reduced mean service time by more than 45 seconds compared to the current mean service time. To perform the hypothesis test, the sample of 48 stores yields the following data (seconds).
90 96 133 108 136 110 119 138
129 98 101 92 135 124 115 90
132 125 110 124 126 138 94 130
108 96 140 135 102 114 109 137
138 104 108 134 92 107 96 119
105 111 96 136 126 116 98 131
Use ? = 0.05
|TS| = ______ |CV| = ______
a 1.548 1.678 Do not reject H?. The mean service time is not reduced by more than 45 seconds. Do not adopt the new process.
b 1.871 1.678 Reject H?. The mean service time is reduced by more than 45 seconds. Adopt the new process.
c 1.871 1.640 Do not reject H?. The mean service time is not reduced by more than 45 seconds. Do not adopt the new process.
d 1.548 1.640 Reject H?. The mean service time is reduced by more than 45 seconds. Adopt the new process.

1.) Which of the following answers represents the objective of a hypothesis test?

a. Rejecting the null hypothesis when it is true.

b. Rejecting the null hypothesis when it is false.

c. Not rejecting the null hypothesis when it is true.

d. Rejecting the null hypothesis when it is false and not rejecting the null hypothesis when it is true.

 

2.) If the chosen significance level is ? = 0.05, then

a. there is a 5% probability of rejecting a true null hypothesis

b. there is a 5% probability of accepting a true null hypothesis

c. there is a 5% probability of rejecting a false null hypothesis

d. there is a 5% probability of accepting a false null hypothesis

(a) In testing hypotheses, which of the following would be strong evidence against the null hypothesis? 

A. Obtaining data with a small P-value. 

B. Obtaining data with a large P-value.

C. Using a small level of line significance.

D. Using a a large level of significance.

(b) The P-value of  a test of a null hypothesis is 

 

A. The probability of the null hypothesis is true.

B. The probability, assuming the null hypothesis is false, that the test statistic will take a value at least as extreme as that actually observed.

C. The probability, assuming the null hypothesis is true, that the test statistic will take a value at least as extreme as that actually observed.

D. The probability of the null hypothesis is false.

(c) In formulating hypotheses for a statistical test of significance, the null hypothesis is often 

A. 0.05 

B. the probability of observing the data you actually obtained 

C. a statement of ''no effect'' or '' no difference''.

D. a statement that the data are 0.