Chapter 8 Tests of Hypotheses Based on a Single Sample
COMPLETION
1. In many situations, the alternative hypothesis is referred to as the hypothesis, since it is the statement
the researcher would really like to validate.
ANS: research
PTS: 1
2. The hypothesis should be identified with the hypothesis of no change, no difference, no improvement,
and son on.
ANS: null
PTS: 1
3. An engineer has suggested a change in the production process in the belief that it will result in a reduced defective
rate. Let p denote the true proportion of defective items resulting from the changed process, and that 5% of items
produced by a manufacturer during a certain period were defective. Then the research hypothesis is the assertion
that
.
ANS: p<.05
PTS: 1
4. In our treatment of hypothesis testing, the hypothesis will always be stated as an equality claim.
ANS: null
PTS: 1
5. The null hypothesis will be rejected if and only if the observed or computed value falls in the
.
ANS: test statistic, rejection region
PTS: 1
6. A error involves not rejecting the null hypothesis is false.
ANS: type II
PTS: 1
7. A error consists of rejecting the null hypothesis is true.
ANS: type I
PTS: 1
8. The probabilities of type I and type II errors are traditionally denoted by the Greek letters and
, , respectively.
ANS:
PTS: 1
9. The rejection region is called if it consists only of large values of the test statistic.
ANS: upper-tailed
PTS: 1
10. The rejection region is called if it consists only of small values of the test statistic.
ANS: lower-tailed
PTS: 1
11. A error is usually more serious than a error.
ANS: type I, type II
PTS: 1
,12. The value that represents the probability of type I error is often referred to as the of the test.
ANS: significance level
PTS: 1
13. If the null hypothesis is then the test statistic value is z = .
ANS: 2
PTS: 1
14. For any significance level the two-tailed rejection region has type I error probability equal
to .
ANS:
PTS:
1
15. Suppose a test procedure about the population mean is performed, when the population is normal with known
standard deviation then if the alternative hypothesis is the rejection region for a level test is
.
ANS:
PTS: 1
16. Suppose a test procedure about the population mean is performed, when the population is normal with known
standard deviation then if the alternative hypothesis is the rejection region for a level test is
.
ANS:
PTS: 1
17. Suppose a test procedure about the population mean is performed, when the population is normal with known
standard deviation then if the alternative hypothesis is the rejection region for a level test is either
or .
ANS:
PTS: 1
18. If is a random sample from a normal distribution, and the sample size n is small, then the standardized
variable has a distribution with degrees of freedom.
ANS: t, n-1
, PTS: 1
19. Suppose a test procedure about the population mean is performed, when the population is normal and the sample
size n is small, then if the alternative hypothesis is the rejection region for a level test is .
ANS:
PTS: 1
20. Suppose a test procedure about the population mean is performed, when the population is normal and the sample
size n is small, then if the alternative hypothesis is the rejection region for a level test is .
ANS:
PTS: 1
21. Suppose a test procedure about the population mean is performed, when the population is normal and the sample
size n is small, then if the alternative hypothesis is the rejection region for a level test is either
or .
ANS:
PTS: 1
22. Let p denote the proportion of individuals in a population who possess a specified property, and X denote the number
of individuals in the sample who possess the same property. Provided that the sample size n is small relative to the
population size, then X has approximately a distribution.
ANS: binomial
PTS: 1
23. Let p denote the proportion of individuals in a population who possess a specified property, and X denote the number
of individuals in the sample who possess the same property. Provided that the sample size n is large, then both X and
the estimator are approximately distributed.
ANS: normally
PTS: 1
24. Let p denote the proportion of individuals in a population who possess a specified property, and X denote the number
of individuals in the sample who possess the same property. The estimator is if
and its standard deviation = .
ANS: unbiased,
PTS: 1
COMPLETION
1. In many situations, the alternative hypothesis is referred to as the hypothesis, since it is the statement
the researcher would really like to validate.
ANS: research
PTS: 1
2. The hypothesis should be identified with the hypothesis of no change, no difference, no improvement,
and son on.
ANS: null
PTS: 1
3. An engineer has suggested a change in the production process in the belief that it will result in a reduced defective
rate. Let p denote the true proportion of defective items resulting from the changed process, and that 5% of items
produced by a manufacturer during a certain period were defective. Then the research hypothesis is the assertion
that
.
ANS: p<.05
PTS: 1
4. In our treatment of hypothesis testing, the hypothesis will always be stated as an equality claim.
ANS: null
PTS: 1
5. The null hypothesis will be rejected if and only if the observed or computed value falls in the
.
ANS: test statistic, rejection region
PTS: 1
6. A error involves not rejecting the null hypothesis is false.
ANS: type II
PTS: 1
7. A error consists of rejecting the null hypothesis is true.
ANS: type I
PTS: 1
8. The probabilities of type I and type II errors are traditionally denoted by the Greek letters and
, , respectively.
ANS:
PTS: 1
9. The rejection region is called if it consists only of large values of the test statistic.
ANS: upper-tailed
PTS: 1
10. The rejection region is called if it consists only of small values of the test statistic.
ANS: lower-tailed
PTS: 1
11. A error is usually more serious than a error.
ANS: type I, type II
PTS: 1
,12. The value that represents the probability of type I error is often referred to as the of the test.
ANS: significance level
PTS: 1
13. If the null hypothesis is then the test statistic value is z = .
ANS: 2
PTS: 1
14. For any significance level the two-tailed rejection region has type I error probability equal
to .
ANS:
PTS:
1
15. Suppose a test procedure about the population mean is performed, when the population is normal with known
standard deviation then if the alternative hypothesis is the rejection region for a level test is
.
ANS:
PTS: 1
16. Suppose a test procedure about the population mean is performed, when the population is normal with known
standard deviation then if the alternative hypothesis is the rejection region for a level test is
.
ANS:
PTS: 1
17. Suppose a test procedure about the population mean is performed, when the population is normal with known
standard deviation then if the alternative hypothesis is the rejection region for a level test is either
or .
ANS:
PTS: 1
18. If is a random sample from a normal distribution, and the sample size n is small, then the standardized
variable has a distribution with degrees of freedom.
ANS: t, n-1
, PTS: 1
19. Suppose a test procedure about the population mean is performed, when the population is normal and the sample
size n is small, then if the alternative hypothesis is the rejection region for a level test is .
ANS:
PTS: 1
20. Suppose a test procedure about the population mean is performed, when the population is normal and the sample
size n is small, then if the alternative hypothesis is the rejection region for a level test is .
ANS:
PTS: 1
21. Suppose a test procedure about the population mean is performed, when the population is normal and the sample
size n is small, then if the alternative hypothesis is the rejection region for a level test is either
or .
ANS:
PTS: 1
22. Let p denote the proportion of individuals in a population who possess a specified property, and X denote the number
of individuals in the sample who possess the same property. Provided that the sample size n is small relative to the
population size, then X has approximately a distribution.
ANS: binomial
PTS: 1
23. Let p denote the proportion of individuals in a population who possess a specified property, and X denote the number
of individuals in the sample who possess the same property. Provided that the sample size n is large, then both X and
the estimator are approximately distributed.
ANS: normally
PTS: 1
24. Let p denote the proportion of individuals in a population who possess a specified property, and X denote the number
of individuals in the sample who possess the same property. The estimator is if
and its standard deviation = .
ANS: unbiased,
PTS: 1
