STATS 9 Quiz | Complete Solution

Instruction

Select True or False for question 1 to 17

1. In tests involving a sample mean or proportion, the alternative hypothesis will state that the population parameter is equal to some value.
2. True    □ False
2. When a claim or assertion is involved in hypothesis testing, the null hypothesis is always the same as the statement itself. □ True    □ False
3. When a null hypothesis can be rejected by an extreme result in one direction only, a two-tail test is appropriate. □ True    □ False
4. An Internal Revenue Service official says, “The percentage of taxpayers who overpay the taxes they owe is considerably less than 10%.”  In the related hypothesis test, we should apply the “Missouri Rule” in setting up the null and alternative hypotheses.
5. True    □ False
5. The level of significance refers to the probability of making a Type I error.
6.   True    □ False
6. For a given sample size, revising a decision rule so that the probability of a Type I error is decreased will also decrease the probability of making a Type II error.

□ True    □ False

7. The first step in hypothesis testing is to determine the critical value(s) of the test statistic.
8. True    □ False
8. Compared to using a = 0.10, the selection of a = 0.001 will tend to make it less likely that a true null hypothesis will be rejected. □ True    □ False
9. If the null and alternative hypotheses are H₀: μ ≤ 100 and H₁: μ >100, the appropriate test will be right-tail. □ True    □ False
10. If the null and alternative hypothesis are H₀: μ = 50 and H₁: μ 50, the appropriate test will be left-tail. □ True    □ False
11. The normal distribution is always used when the null hypothesis involves a population mean. □ True    □ False
12. In practice, the population standard deviation is usually known, making it unnecessary to approximate its value with the sample standard deviation, s. □ True    □ False
13. For tests involving a proportion, the normal distribution is considered to be appropriate as an approximation for the binomial distribution whenever nπ ³ 5 and n(1 – π) ³ 5.
14. True    □ False
14. Failure to reject a null hypothesis does not constitute proof that it is true, but rather indicates that we are unable to reject it at the level of significance being used for the test. □ True    □ False
15. The p-Value in hypothesis testing corresponds to the significance level where a critical value of the test statistic is exactly the same as the calculated value. □ True    □ False
16. The p-Value for a certain hypothesis test is 0.13.  If we were to evaluate the results at a significance level of 0.10, the null hypothesis would be rejected. □ True    □ False
17. The power of a test refers to the probability that the test will correctly reject a null hypothesis that is false. □ True    □ False

PART B

Circle the correct answer for questions 18 to 33.

18. In hypothesis testing, the null hypothesis is a statement assumed to be

1. true unless we have strong evidence that it is false.
2. false unless we have strong evidence that it is true.
3. true regardless of the nature of our evidence.
4. false regardless of the nature of our evidence.

19. Whenever the null hypothesis is not rejected, the alternative hypothesis

1. is also not rejected.
2. is rejected.
3. must be revised.
4. replaces the null hypothesis.

20. “Well over 70% of last year’s graduates have jobs in their field of study.”  If the “Missouri Rule” is applied to the related hypothesis test, the null and alternative hypotheses will be:

1. H₀: π ³ 0.70, H₁: π < 0.70.
2. H₀: π < 0.70, H₁: π ³ 0.70.
3. H₀: π = 0.70, H₁: π ¹ 0.70.
4. H₀: π ≤ 0.70, H₁: π > 0.70.

21. The probability of rejecting a true null hypothesis is

1. the significance level of the test.
2. the power of the test.
3. always less than 0.20 for two-tail tests.
4. None of the preceding.

22. In hypothesis testing, the decision rule is based on calculated versus critical value(s) for the

1. population parameter.                   c. sample size.
2. test statistic.                                  d. power of the test.

23. “The proportion of business-improvement loan applications turned down in this state is no more than 15%.”  If the null hypothesis is H_0:  π ≤ 0.15, the appropriate alternative hypothesis is

1. H₁: π ¹ 0.15.                     c. H₁: π = 0.15.
2. H₁: π > 0.15.                    d. H₁: π < 0.15.

24. The population from which a random sample has been selected is normally distributed.  For a hypothesis test involving the sample mean, the t-test should be used instead of the z-test if

1. n < 30 and standard deviation of the population is not known.
2. n ³ 30 and standard deviation of the population is unknown.
3. n < 30 and standard deviation of the population is known.
4. Both (a) and (b).

25. “The average management consultant spends $750 per year on industry publications and seminar attendance to stay abreast of developments in the field.”  In evaluating the null hypothesis derived from this assertion, the appropriate test would be

1. two-tail.                             c. right-tail.
2. left-tail                              d. None of the preceding.

26. In a right-tail test with H₀: μ ≤ 100 and H₁: μ > 100, the sample mean is x = 150.  The null hypothesis.

1. should be rejected.
2. should be rejected only if n ³ 30.
3. should not be rejected.
4. not enough information is given.

27. In testing H₀ : π ≤ 0.30 against H₁ : π > 0.30, the critical value of the test statistic is
26. = +1.96.  If the sample proportion is p = 0.35 and the standard error of the sample proportion is  = 0.02, the appropriate conclusion would be to

1. reject H_0.
2. fail to reject both H₀ and H₁.
3. fail to reject H₀.
4. reject both H₀ and H₁.

28. An inventor claims that her new device will “drastically reduce” the oil consumption of gasoline-powered vehicles in a corporate fleet.  Currently, the average vehicle requires 2.3 quarts of oil between changes.  The appropriate null and alternative hypotheses in evaluating her claim will be

1. H₀: μ ³ 2.3 and H₁: μ < 2.3.
2. H₀: μ ≤ 2.3 and H₁: μ > 2.3.
3. H₀: μ ≤ 2.3 and H₁: μ < 2.3.
4. H₀: μ = 2.3 and H₁: μ ¹ 2.3.

29. In a given hypothesis test, the null hypothesis cannot be rejected at the 0.025 and 0.01 levels, but can be rejected at the 0.05 and 0.10 levels.  The most accurate statement we can make about the p-Value for this test is

1. p-Value = 0.05.
2. p-Value > 0.10.
3. 0.025 < p-Value < 0.05.
4. 0.05 < p-Value < 0.10.

30. In a one-tail test involving a sample mean, the p-Value is found to be equal to 0.10.  If the test had been two-tail instead of one-tail, the p-Value would have been

a. 0.20b. 0.10.c. 0.05.d. 0.025.

31. Based on sample data, the 95% confidence interval for the population mean is from $150 to $250.  If the a = 0.05 level of significance were used in testing H₀: μ = $260 versus H₁: μ ¹ $260, the null hypothesis

1. would be rejected.
2. would not be rejected.
3. would have to be revised.
4. Not enough information is given.

32. The power of a test is the probability that it will

1. reject a true null hypothesis.
2. reject a false null hypothesis
3. fail to reject a true null hypothesis
4. fail to reject a false null hypothesis

33. For a given level of significance (a), increasing the sample size will

1. reduce the probability of making a Type I error.
2. reduce the probability of making a Type II error.
3. have no effect on the probability of making either type of error.
4. Both (a) and (b).