1. For a sample size of 30, changing from using the standard normal distribution to using the t distribution in a hypothesis test, A. will result in the area corresponding to the critical value being smaller.
2. When the null hypothesis is rejected, it is A. possible a Type I error has occurred
3. • A Type I error is rejecting H0 when it is true.
• The probability of making a Type I error when the null hypothesis is true as an equality is called the level of significance.
• Applications of hypothesis testing that only control for the Type I error are often called significance tests. A. Type I Error
4. A grocery store has an average sales of $8000 per day. The store introduced several advertising campaigns in order to increase sales. To determine whether or not the advertising campaigns have been effective in increasing sales, a sample of 64 days of sales was selected. It was found that the average was $8300 per day. From past information, it is known that the standard deviation of the population is $1200. The correct null hypothesis for this problem is A. μ < 8000.
5. A pharmaceutical manufacturer has come up with a new drug intended to provide greater headache relief than the old formula. Of 250 patients treated with the previous medication, 130 reported “fast relief from headache pain.” Of 200 individuals treated with the new formula, 128 said they got “fast relief.” At the 0.05 level, What is the calculated value of the pooled estimate of the population proportion? (Specify your answer to the 3rd decimal.) A. .573
6. A pharmaceutical manufacturer has come up with a new drug intended to provide greater headache relief than the old formula. Of 250 patients treated with the previous medication, 130 reported “fast relief from headache pain.” Of 200 individuals treated with the new formula, 128 said they got “fast relief.” At the 0.05 level, What is the calculated value of the test statistic? (Specify your answer to the 2nd decimal.) A. -2.56\
7. A pharmaceutical manufacturer has come up with a new drug intended to provide greater headache relief than the old formula. Of 250 patients treated with the previous medication, 130 reported “fast relief from headache pain.” Of 200 individuals treated with the new formula, 128 said they got “fast relief.” At the 0.05 level, What is your conclusion based on calculated value of test statistic and critical value? A. Reject H0
8. A scrap metal dealer claims that the mean of his cash scales is “no more than $80,” but an Internal Revenue Service agent believes the dealer is untruthful. Observing a sample of 20 cash customers, the agent finds the mean purchases to be $91, with a standard deviation of $21. Assuming the population is approximately normally distributed, and using the 0.05 level of significance, what is the calculated value of test statistic? (Specify your answer to the 3rd decimal.) A. 2.34
9. A scrap metal dealer claims that the mean of his cash scales is “no more than $80,” but an Internal Revenue Service agent believes the dealer is untruthful. Observing a sample of 20 cash customers, the agent finds the mean purchases to be $91, with a standard deviation of $21. Assuming the population is approximately normally distributed, and using the 0.05 level of significance, what is the critical value? (Specify your answer to the 3rd decimal.) A. 1.729
10. A scrap metal dealer claims that the mean of his cash scales is “no more than $80,” but an Internal Revenue Service agent believes the dealer is untruthful. Observing a sample of 20 cash customers, the agent finds the mean purchases to be $91, with a standard deviation of $21. Assuming the population is approximately normally distributed, and using the 0.05 level of significance, What is your conclusion based on calculated value of test statistic and critical value? A. Reject H0
11. 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 A. H0: μ 85 Ha: μ < 85.
12. A two-tailed test is performed at the .05 level of significance. The p-value is determined to be .09. The null hypothesis A. should not be rejected.
13. A Type II error is accepting H0 when it is false.
• It is difficult to control for the probability of making a Type II error.
• Statisticians avoid the risk of making a Type II error by using “do not reject H0” and not “accept H0”. A. Type II Error
16. As the test statistic becomes larger, the p-value A. gets smaller
17. Compute the p-value using the following three steps:
1. Compute the value of the test statistic z.
2. If z is in the upper tail (z > 0), compute the probability that z is greater than or equal to the value of the test statistic. If z is in the lower tail (z < 0), compute the probability that z is less than or equal to the value of the test statistic.
3. Double the tail area obtained in step 2 to obtain the p-value.
• The rejection rule: Reject H0 if the p-value < a. A. p-Value Approach to Two-Tailed Hypothesis Testing
18. For a lower tail test, the test statistic z is determined to be zero. The p-value for this test is A. +.5
19. For a one-tailed (upper tail) hypothesis test with a sample size of 18 and a .05 level of significance, the critical value of the test statistic t is A. 1.740
20. For a sample of 35 items from a population for which the standard deviation is 20.5, the sample mean is 458. At the 0.05 level of significance, test H0: µ = 450 verses H1: µ ≠ 450.
What is the calculated value of test statistic? (Specify your answer to the 2nd decimal.) A. 2.31
21. For a sample of 35 items from a population for which the standard deviation is 20.5, the sample mean is 458. At the 0.05 level of significance, test H0: µ = 450 verses H1: µ ≠ 450. What is your conclusion based on calculated value of test statistic and critical value? A. Reject H0
22. For a sample of 35 items from a population for which the standard deviation is 20.5, the sample mean is 458. What is the lower limit of the confidence interval, if you construct a 95% confidence interval for the population mean? (Specify your answer to the 2nd decimal.) A. 451.21
23. For a sample of 35 items from a population for which the standard deviation is 20.5, the sample mean is 458. What is the upper limit of the confidence interval, if you construct a 95% confidence interval for the population mean? (Specify your answer to the 2nd decimal.) A. 464.79
24. For a sample of 48 finance majors, the average time spent reading each issue of the campus newspaper is 19.7 minutes, with a standard deviation of 7.3 minutes. The corresponding figures for a sample of 40 management information system majors are 16.3 and 4.1 minutes. What is the the test statistic, t, with the 0.01 level of significance? (Specify your answer to the 2nd decimal.) A. 2.749
25. For a sample of 48 finance majors, the average time spent reading each issue of the campus newspaper is 19.7 minutes, with a standard deviation of 7.3 minutes. The corresponding figures for a sample of 40 management information system majors are 16.3 and 4.1 minutes. What is the the degree of freedom with the 0.01 level of significance? (Specify your answer to the 2nd decimal.) A. 76.16
26. For a sample of 48 finance majors, the average time spent reading each issue of the campus newspaper is 19.7 minutes, with a standard deviation of 7.3 minutes. The corresponding figures for a sample of 40 management information system majors are 16.3 and 4.1 minutes. Using the 0.01 level of significance, What is your conclusion based on calculated value of test statistic and critical value? A. Reject H0
27. Generally, the ________ sample procedure for inferences about two population means provides better precision than the _______ sample approach. A. matched, independent
28. If the cost of making a Type I error is high, a smaller value should be chosen for the A. level of significance.
29. If the level of significance of a hypothesis test is raised from .01 to .05, the probability of a Type II error A. will decrease
30. In a one-tailed hypothesis test (lower tail), the test statistic is determined to be -2. The p-value for this test is A. .0228
31. In the hypothesis testing procedure, α is the A. level of significance.
32. In the past, 44% of those taking a public accounting qualifying exam have passed the exam on their first try. Latterly, the availability of exam preparation books and tutoring sessions may have improved the likelihood of an individual’s passing on his first try. In a sample of 250 recent applicants, 130 passed on their first attempt. At the 0.05 level of significance, what is the calculated value of test statistic? (Specify your answer to the 2nd decimal.) A. 2.55
33. In the past, 44% of those taking a public accounting qualifying exam have passed the exam on their first try. Latterly, the availability of exam preparation books and tutoring sessions may have improved the likelihood of an individual’s passing on his first try. In a sample of 250 recent applicants, 130 passed on their first attempt. At the 0.05 level of significance, what is the p-value based on value of test statistic? (Specify your answer to the 4th decimal.) A. .0054
34. In the past, 44% of those taking a public accounting qualifying exam have passed the exam on their first try. Latterly, the availability of exam preparation books and tutoring sessions may have improved the likelihood of an individual’s passing on his first try. In a sample of 250 recent applicants, 130 passed on their first attempt. At the 0.05 level of significance, What is your conclusion based on P-value calculated from the value of test statistic? A. Reject H0
35. Independent random samples of vehicles traveling past a given point on an interstate highway have been observed on Monday versus Wednesday. For 16 cars observed on Monday, the average speed was 59.4 mph, with a standard deviation of 3.7 mph. For 20 cars observed on Wednesday, the average speed was 56.3 mph, with a standard deviation of 4.4 mph. At the 0.05 level, and assuming normal populations, what is the calculated value of test statistic, t? (Specify your answer to the 3rd decimal.) A. 2.296
36. Independent random samples of vehicles traveling past a given point on an interstate highway have been observed on Monday versus Wednesday. For 16 cars observed on Monday, the average speed was 59.4 mph, with a standard deviation of 3.7 mph. For 20 cars observed on Wednesday, the average speed was 56.3 mph, with a standard deviation of 4.4 mph. At the 0.05 level, and assuming normal populations, what is the calculated value of degree of freedom? (Specify your answer to the 2nd decimal.) A. 33.89
37. Independent random samples of vehicles traveling past a given point on an interstate highway have been observed on Monday versus Wednesday. For 16 cars observed on Monday, the average speed was 59.4 mph, with a standard deviation of 3.7 mph. For 20 cars observed on Wednesday, the average speed was 56.3 mph, with a standard deviation of 4.4 mph. At the 0.05 level, and assuming normal populations, what is your conclusion based on calculated value of test statistic and critical value? A. Reject H0 and conclude that speeds are faster on Monday than on Wednesday
38. Lower tail: Reject H0 if z < or = to -za
• Upper tail: Reject H0 if z > or = to za A. • The rejection rule is (critical value):
39. Read the t statistic from the t distribution table and circle the correct answer. For a one-tailed test (upper tail) with a sample size of 26 and at the .10 level, t = A. 1.316
40. Read the z statistic from the normal distribution table and circle the correct answer. For a one-tailed test (upper tail) at α = .0630, z = A. 1.53
41. Read the z statistic from the normal distribution table and circle the correct answer. For a two-tailed test using α = .1388, z = A. 1.48
42. Read the z statistic from the normal distribution table and circle the correct answer. For a one-tailed test (upper tail) using α = .1230, z = A. 1.16
43. Read the z statistic from the normal distribution table and circle the correct answer. For a one-tailed test (lower tail) using α = .1020, z = A. -1.27
44. Regarding inferences about the difference between two population means, the sampling design that uses a pooled sample variance in cases of equal population standard deviations is based on A. independent samples.
45. Rejection Rule: p -Value Approach
Reject H0 if p -value < or = to a
Rejection Rule: Critical Value Approach
H0: µ > or = to µ0= Reject H0 if t < -ta
H0: µ < or = to µ0 =Reject H0 if t > or = to ta
H0: µ = µ0 Reject H0 if t < – ta/2 or t > ta/2 A. Tests About a Population Mean: s Unknown
46. Salary information regarding male and female employees of a large company is shown below. The point estimate of the difference between the means of the two populations is A. 3
47. Step 1. Develop the null and alternative hypotheses.
Step 2. Specify the level of significance a.
Step 3. Collect the sample data and compute the value of the test statistic. p-Value Approach Step 4. Use the value of the test statistic to compute the p-value.
Step 5. Reject H0 if p-value < or = to a. Critical Value Approach Step 4. Use the level of significance a to determine the critical value and the rejection rule. Step 5. Use the value of the test statistic and the rejection rule to determine whether to reject H0 A. Steps of Hypothesis Testing
48. Suspecting that television repair shops tend to charge women more than they do men, Emily disconnected the speaker wire on her portable television and took it to a sample of 12 shops. She was given repair estimates that averaged $85, with a standard deviation of $28. Her friend John, taking the same set to another sample of 9 shops, was provided with an average estimate of $65, with a standard deviation of $21. Assuming normal populations with equal standard deviations, What is the the pooled estimate of the common variance with the 0.05 level? (Specify your answer to the 3rd decimal.) A. 639.579
49. Suspecting that television repair shops tend to charge women more than they do men, Emily disconnected the speaker wire on her portable television and took it to a sample of 12 shops. She was given repair estimates that averaged $85, with a standard deviation of $28. Her friend John, taking the same set to another sample of 9 shops, was provided with an average estimate of $65, with a standard deviation of $21. Assuming normal populations with equal standard deviations, What is the the test statistic, t, with the 0.05 level? (Specify your answer to the 3rd decimal.) A. 1.793
50. Suspecting that television repair shops tend to charge women more than they do men, Emily disconnected the speaker wire on her portable television and took it to a sample of 12 shops. She was given repair estimates that averaged $85, with a standard deviation of $28. Her friend John, taking the same set to another sample of 9 shops, was provided with an average estimate of $65, with a standard deviation of $21. Assuming normal populations with equal standard deviations, What is your conclusion based on calculated value of test statistic and critical value? A. Reject H0
51. The average length of a flight by regional airlines in the United States has been reported as 464 miles. If a simple random sample of 30 flights by regional airlines were to have a mean of 479.6 miles and a standard deviation of 42.8 miles, if we want to test whether this would tend to cast doubt on the reported average of 464 miles, what is the calculated value of test statistic? (Specify your answer to the 3rd decimal.) A. 1.996
52. The average length of a flight by regional airlines in the United States has been reported as 464 miles. If a simple random sample of 30 flights by regional airlines were to have a mean of 476.9 miles and a standard deviation of 42.8 miles, would this tend to cast doubt on the reported average of 464 miles? Use a two-tail test and the 0.05 level of significance in arriving at your answer. A. Do not reject H0 which states that at the 0.05 level, the results do not cause us to doubt that the average length of a flight by regional airlines in the U.S. is the reported value, 464 miles.
53. The average monthly rent for one-bedroom apartments in Chattanooga has been $700. Because of the downturn in the real estate market, it is believed that there has been a decrease in the average rental. The correct hypotheses to be tested are A. H0: μ ≥ 700 Ha: μ < 700
54. The critical value of t for a two-tailed test with 6 degrees of freedom using α = .05 is A. 2.447
55. The critical values will occur in both the lower and upper tails of the standard normal curve.
• Use the standard normal probability distribution table to find za/2 (the z-value with an area of a/2 in the upper tail of the distribution).
• The rejection rule is: Reject H0 if z < -za/2 or z > za/2. A. Critical Value Approach to Two-Tailed Hypothesis Testing
56. The developer of a new welding rod claims that spot welds using his product will have greater strength than conventional welds. For 45 welds using the new rod, the average tensile strength is 23,500 pounds per square inch, with a standard deviation of 600 pounds. For 40 conventional welds on the same materials, the average tensile strength is 23,140 pounds per square inch, with a standard deviation of 750 pounds. Using the 0.01 level, what is the calculated value of t statistic? (Specify your answer to the 3rd decimal.) A. 2.424
57. The developer of a new welding rod claims that spot welds using his product will have greater strength than conventional welds. For 45 welds using the new rod, the average tensile strength is 23,500 pounds per square inch, with a standard deviation of 600 pounds. For 40 conventional welds on the same materials, the average tensile strength is 23,140 pounds per square inch, with a standard deviation of 750 pounds. Using the 0.01 level, what is the calculated value of degree of freedom? (Specify your answer to the 2nd decimal.) A. 74.6
58. The developer of a new welding rod claims that spot welds using his product will have greater strength than conventional welds. For 45 welds using the new rod, the average tensile strength is 23,500 pounds per square inch, with a standard deviation of 600 pounds. For 40 conventional welds on the same materials, the average tensile strength is 23,140 pounds per square inch, with a standard deviation of 750 pounds. Using the 0.01 level, what is your conclusion based on calculated value of test statistic and critical value? A. Reject H0
59. The following information was obtained from matched samples taken from two populations. Assume the population of differences is normally distributed. The null hypothesis tested is H0: μd = 0. The test statistic for the difference between the two population means is
Individual A. -1
60. The following information was obtained from matched samples taken from two populations. Assume the population of differences is normally distributed.
Method 1
7,5,6,7,5
Method 2
5,9,8,7,6
The 95% confidence interval for the difference between the two population means is A. -3.776 to 1.776
61. The probability of committing a Type I error when the null hypothesis is true as an equality is A. the level of significance.
62. The p-value is the probability, computed using the test statistic, that measures the support (or lack of support) provided by the sample for the null hypothesis.
• If the p-value is less than or equal to the level of significance a, the value of the test statistic is in the rejection region.
Reject H0 if the p-value < a A. p-Value Approach to One-Tailed Hypothesis Testing
63. The p-value is. A. a probability.
64. The results of a recent poll on the preference of shoppers regarding two products are shown below.
Product
Shoppers Surveyed
Shoppers FavoringThis Product
A
800
560
B
900
612
At 95% confidence, the margin of error is A. .044
65. The test statistic z has a standard normal probability distribution.
• We can use the standard normal probability distribution table to find the zvalue with an area of a in the lower (or upper) tail of the distribution.
• The value of the test statistic that established the boundary of the rejection region is called the critical value for the test. A. Critical Value Approach to One-Tailed Hypothesis Testing
66. When the p-value is used for hypothesis testing, the null hypothesis is rejected if A. p-value &λτ; α.
67. 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 A. H0: μ 10.0% Ha: μ < 10.0%
68. z/2 and -z/2: reject h0 if z <-z/2 or z>z/2
z: reject h0 if z > z/2
-z: reject h0 if z < -z/2 A. One-Tailed Tests About a Population Mean: s Known Decision Rule
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