Ch. 9 hypothesis test

37. When the hypotheses H0: μ ≥ 100 and Ha: μ < 100 are being tested at a level of significance of α, the null hypothesis will be rejected if the test statistic z is _____.

(< with line under it) < -zα

53. Read the t statistic from the table of t distributions and circle the correct answer. A one-tailed test (lower tail), a sample size of 10 at a .10 level of significance; t = _____.

-1.383

79. For a two-tailed hypothesis test with a test statistic value of z = 2.05, the p-value is _____.

.0404

48. When using Excel to calculate a p-value for an upper-tail hypothesis test, which of the following must be used?

1 − NORM.S.DIST

36. Read the z statistic from the normal distribution table and circle the correct answer. A one-tailed test (upper tail) at a .123 level of significance; z = _____.

1.16

55. The school's newspaper reported that the proportion of students majoring in business is at least 30%. You plan on taking a sample to test the newspaper's claim. The correct set of hypotheses is _____.

H0: p ≥ .30 Ha: p < .30

5. Which of the following hypotheses is not a valid null hypothesis?

H0: μ < 0

19. A soft drink filling machine, when in perfect adjustment, fills the bottles with 12 ounces of soft drink. Any overfilling or underfilling results in the shutdown and readjustment of the machine. To determine whether or not the machine is properly adjusted, the correct set of hypotheses is _____.

H0: μ = 12 Ha: μ ≠ 12

16. A meteorologist stated that the average temperature during July in Chattanooga was 80 degrees. A sample of July temperatures over a 32-year period was taken. The correct set of hypotheses is _____.

H0: μ = 80 Ha: μ ≠ 80

18. The average life expectancy of tires produced by Whitney Tire Company has been 40,000 miles. Management believes that due to a new production process, the life expectancy of its tires has increased. In order to test the validity of this belief, the correct set of hypotheses is _____.

H0: μ ≤ 40,000 Ha: μ > 40,000

20. The manager of an automobile dealership is considering a new bonus plan in order to increase sales. Currently, the mean sales rate per salesperson is five automobiles per month. The correct set of hypotheses for testing the effect of the bonus plan is _____.

H0: μ ≤ 5 Ha: μ > 5

15. Your investment executive claims that the average yearly rate of return on the stocks she recommends is at least 10.0%. You plan on taking a sample to test her claim. The correct set of hypotheses is _____.

H0: μ ≥ 10.0% Ha: μ < 10.0%

17. A student believes that the average grade on the final examination in statistics is at least 85. She plans on taking a sample to test her belief. The correct set of hypotheses is _____.

H0: μ ≥ 85 Ha: μ < 85

47. Excel's __________ function can be used to calculate a p-value for a hypothesis test.

NORM.S.DIST

58. Which Excel function would NOT be appropriate to use when conducting a hypothesis test for a population proportion?

STDEV

54. Excel's __________ function can be used to calculate a p-value for a hypothesis test when σ is unknown.

T.DIST

25. A Type II error is committed when _____.

a true alternative hypothesis is mistakenly rejected

Exhibit 9-4 A random sample of 16 students selected from the student body of a large university had an average age of 25 years. We want to determine if the average age of all the students at the university is significantly different from 24. Assume the distribution of the population of ages is normal with a standard deviation of 2 years. 69. refer to exhibit 9-4. At a .05 level of significance, it can be concluded that the mean age is ____________.

not significantly different from 24

21. In hypothesis testing if the null hypothesis is rejected, _____.

the evidence supports the alternative hypothesis

38. In order to test the hypotheses H0: μ ≤ 100 and Ha: μ > 100 at an α level of significance, the null hypothesis will be rejected if the test statistic z is _____.

≥ zα

34. Read the z statistics from the normal distribution table and circle the correct answer. A two-tailed test at a .0694 level of significance; z = _____.

-1.48 and 1.48

35. Read the z statistic from the normal distribution table and circle the correct answer. A one-tailed test (lower tail) at a .063 level of significance; z = _____.

-1.53

Exhibit 9-2 The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took the customers in the sample to check out was 3.1 minutes. The population standard deviation is known to be 0.5 minute. We want to test to determine whether or not the mean waiting time of all customers is significantly more than 3 minutes. 63. Refer to Exhibit 9-2. The p-value is _____.

.0228

Exhibit 9-6 A random sample of 100 people was taken. Eighty of the people in the sample favored Candidate A. We are interested in determining whether or not the proportion of the population in favor of Candidate A is significantly more than 75%. 74. Refer to Exhibit 9-6. The p-value is _____.

.1251

Exhibit 9-6 A random sample of 100 people was taken. Eighty of the people in the sample favored Candidate A. We are interested in determining whether or not the proportion of the population in favor of Candidate A is significantly more than 75%. 73. Refer to Exhibit 9-6. The test statistic is _____.

1.25

51. Read the t statistic from the table of t distributions and circle the correct answer. A two-tailed test, a sample of 20 at a .20 level of significance; t = _____.

1.328

52. Read the t statistic from the table of t distributions and circle the correct answer. A one-tailed test (upper tail), a sample size of 18 at a .05 level of significance; t = _____.

1.740

Exhibit 9-2 The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took the customers in the sample to check out was 3.1 minutes. The population standard deviation is known to be 0.5 minute. We want to test to determine whether or not the mean waiting time of all customers is significantly more than 3 minutes. 62. Refer to Exhibit 9-2. The test statistic is _____.

2.00

Exhibit 9-4 A random sample of 16 students selected from the student body of a large university had an average age of 25 years. We want to determine if the average age of all the students at the university is significantly different from 24. Assume the distribution of the population of ages is normal with a standard deviation of 2 years. 68. Refer to Exhibit 9-4. The test statistic is _____.

2.00

56. In the past, 75% of the tourists who visited Chattanooga went to see Rock City. The management of Rock City recently undertook an extensive promotional campaign. They are interested in determining whether the promotional campaign actually INCREASED the proportion of tourists visiting Rock City. The correct set of hypotheses is _____.

H0: p ≤ .75 Ha: p > .75

57. The academic planner of a university thinks that at least 35% of the entire student body attends summer school. The correct set of hypotheses to test his belief is _____.

H0: p ≥ .35 Ha: p < .35

49. When using Excel to calculate a p-value for a lower-tail hypothesis test, which of the following must be used?

NORM.S.DIST

22. If a hypothesis test leads to the rejection of the null hypothesis, a _____.

Type I error may have been committed

30. The level of significance is symbolized by _____.

a

23. The error of rejecting a true null hypothesis is _____.

a Type I error

31. In hypothesis testing, the critical value is _____.

a number that establishes the boundary of the rejection region

4. A Type I error is committed when _____.

a true null hypothesis is rejected

42. If a hypothesis is not rejected at a 5% level of significance, it will _____.

also not be rejected at the 1% level

3. As a general guideline, the research hypothesis should be stated as the _____.

alternative hypothesis

40. For a two-tailed test with a sample size of 40, the null hypothesis will NOT be rejected at a 5% level of significance if the test statistic is _____.

between -1.96 and 1.96, exclusively

76. For a two-tailed hypothesis test about a population mean, the null hypothesis can be rejected if the confidence interval _____.

does not include µ0

39. For a one-tailed test (upper tail) with a sample size of 900, the null hypothesis will be rejected at the .05 level of significance if the test statistic is _____.

greater than or equal to 1.645

81. The smaller the p-value, the _____.

greater the evidence against H0

6. The practice of concluding "do not reject H0" is preferred over "accept H0" when we _____.

have not controlled for the Type II error

12. An example of statistical inference is _____.

hypothesis testing

9. In tests about a population proportion, p0 represents the _____.

hypothesized population proportion

33. A two-tailed test is a hypothesis test in which the rejection region is _____.

in both tails of the sampling distribution

32. A one-tailed test is a hypothesis test in which rejection region is _____.

in one tail of the sampling distribution

80. The rejection region for a one-tailed hypothesis test _____.

is in the tail that supports the alternative hypothesis

77. In a two-tailed hypothesis test, the null hypothesis should be rejected if the p-value is _____.

less than or equal to a

8. When the rejection region is in the lower tail of the sampling distribution, the p-value is the area under the curve _____.

less than or equal to the test statistic

7. If the cost of a Type I error is high, a smaller value should be chosen for the _____.

level of significance

11. For a two-tailed hypothesis test about μ, we can use any of the following approaches EXCEPT compare the _____ to the _____.

level of significance; confidence coefficient

27. The level of significance is the _____.

maximum allowable probability of a Type I error

41. If a hypothesis is rejected at a 5% level of significance, it _____.

may be rejected or not rejected at the 1% level

Exhibit 9-6 A random sample of 100 people was taken. Eighty of the people in the sample favored Candidate A. We are interested in determining whether or not the proportion of the population in favor of Candidate A is significantly more than 75%. 75. Refer to Exhibit 9-6. At a .05 level of significance, it can be concluded that the proportion of the population in favor of candidate A is _____.

not significantly greater than 75%

2. Two approaches to drawing a conclusion in a hypothesis test are _____.

p-value and critical value

45. When the p-value is used for hypothesis testing, the null hypothesis is rejected if _____.

p-value ≤ α

43. A p-value is the _____.

probability, when the null hypothesis is true, of obtaining a sample result that is at least as unlikely as what is observed

28. The level of significance in hypothesis testing is the probability of _____.

rejecting a true null hypothesis

46. A two-tailed test is performed at a 5% level of significance. The p-value is determined to be .09. The null hypothesis _____.

should not be rejected

Exhibit 9-2 The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took the customers in the sample to check out was 3.1 minutes. The population standard deviation is known to be 0.5 minute. We want to test to determine whether or not the mean waiting time of all customers is significantly more than 3 minutes. 64. Refer to Exhibit 9-2. At a .05 level of significance, it can be concluded that the mean of the population is _____.

significantly greater than 3

1. More evidence against H 0 is indicated by _____.

smaller p-values

24. In hypothesis testing, if the null hypothesis has been rejected when the alternative hypothesis has been true, _____.

the correct decision has been made

14. In hypothesis testing, the alternative hypothesis is _____.

the hypothesis concluded to be true if the null hypothesis is rejected

29. In the hypothesis testing procedure, α is _____.

the level of significance

44. Which of the following does NOT need to be known in order to compute the p-value?

the level of significance

13. In hypothesis testing, the hypothesis tentatively assumed to be true is _____.

the null hypothesis

78. If a hypothesis test has a Type I error probability of .05, that means if the null hypothesis is _____.

true, it will be rejected 5% of the time

50. For a sample size of 30, changing from using the standard normal distribution to using the t distribution in a hypothesis test _____.

will result in the rejection region being smaller

26. The probability of making a Type I error is denoted by _____.

α