81 Multiple Choice Questions with Answers - Hypothesis Testing | SPEA, Exams of Environmental Science

Download 81 Multiple Choice Questions with Answers - Hypothesis Testing | SPEA and more Exams Environmental Science in PDF only on Docsity! Chapter 8 - Hypothesis Testing 1. There is one and only one correct method to perform a hypothesis test procedure. Ans: False 2. The null hypothesis states that there is no difference between a parameter and a specific value, or that there is no difference between two parameters. Ans: True 3. Is the statement 0H : = 9 a valid null hypothesis? A) Yes, this is a statement that compares a parameter to a value B) Yes, this is a statement that compares two parameters C) No, equalities are not permitted in a null hypothesis D) No, there is no parameter contained in this statement Ans: D 4. Is the statement 0H : 13 = 8 a valid null hypothesis? A) Yes, this is a statement that compares a parameter to a value B) Yes, this is a statement that compares two parameters C) No, equalities are not permitted in a null hypothesis D) No, there is no parameter contained in this statement Ans: D 5. Is the statement 0H :  = 9 a valid null hypothesis? A) Yes, this is a statement that compares a parameter to a value B) Yes, this is a statement that compares two parameters C) No, equalities are not permitted in a null hypothesis D) No, there is no parameter contained in this statement Ans: A 6. Are the following statements 0H : = 6 AH :  6 a valid pair of null and alternative hypothesis? A) No, there are no parameters contained in these statements B) No, the alternative hypothesis cannot contain numeric values C) Yes, these statements are two non-overlapping hypotheses and compare two parameters D) Yes, these statements are two non-overlapping hypotheses and compare a Page 85 Chapter 8 - Hypothesis Testing parameter to a value Ans: A 7. Are the following statements 0H :   12 AH :   16 a valid pair of null and alternative hypothesis? A) No, there are no parameters contained in these statements B) No, the alternative hypothesis cannot contain numeric values C) No, these statements have overlapping regions D) No, these statements both compare a parameter to a value Ans: C 8. Are the following statements 0H :  6 AH :   6 a valid pair of null and alternative hypothesis? A) No, there are no parameters contained in these statements B) No,  cannot be a parameter C) Yes, these statements have two non-overlapping hypotheses and compare a parameter to a value D) Yes, these statements have two non-overlapping hypotheses and compare two parameters Ans: C 9. Sandra Johnson, a researcher, believes her pulse rate will decrease with exercise. Her alternative hypothesis would contain an equal sign. Ans: False 10. If the null hypothesis is not rejected when it is false, a type II error has been committed. Ans: True 11. The probability of committing a type II error is symbolized by  . Ans: True 12. The numerical value obtained from a statistical test is called the __________. Ans: test value 13. A type I error occurs if one rejects the null hypothesis when it is __________. Ans: true 14. A type II error occurs if one does not reject the null hypothesis when it is __________. Ans: false Page 86 Chapter 8 - Hypothesis Testing 27. Which type of alternative hypothesis is used in the figure below? A) H k1:  B) H k1:  C) H k1:  D) H k1:  Ans: C 28. Using the z table in Table E of Appendix C, determine the critical value for the left- tailed test with  0 02. . A) 2.33 B) 2.05 C)  2 33. D)  2 05. Ans: D 29. Using the z table in Table E of Appendix C, what are the critical values for a two-tailed test when  0 03. . A) ± 1.88 B) ± 2.17 C) ± 2.05 D) ± 2.33 Ans: B 30. Using the z table in Table E of Appendix C, determine the critical value for the right- tailed test with  0 035. . A) 0.39 B) 2.05 C) 1.81 D) 2.11 Ans: C 31. A recent gasoline survey said that the national average price of gasoline was $1.498 a gallon. It was felt that gasoline in Texas was significantly lower than the national average. A survey of 10 different suburbs in Dallas, Texas found the average price of gasoline to be $1.294 a gallon with a standard deviation of $0.0526. What is the critical value using  0 01. ? A) 1.26 B) 2.33 C) –1.26 D) –2.33 Ans: D 32. Using the z table found in Table E of Appendix C, the critical value for the right-tailed test with  0 03. is 1.88. Ans: True 33. Stating the hypothesis is the first step used in hypothesis testing. Ans: True 34. If the null hypothesis is not rejected, then it must be true. Ans: False Page 89 Chapter 8 - Hypothesis Testing 35. If the observed value is 11, the expected value is 7, and the standard error is 4, then the test value used for the z test is equal to A) 1.00 B) 4.00 C) –4.00 D) –1.00 Ans: A 36. If the observed value is 5, the expected value is 7, and the standard error is 3, then the test value used for the z test is equal to A) 0.67 B) 2.00 C) –2.00 D) –0.67 Ans: D Use the following to answer questions 37-38: A recent survey indicated that the average amount spent for breakfast by business managers was $7.58 with a standard deviation of $0.42. It was felt that breakfasts on the West Coast were higher than $7.58. A sample of 81 business managers on the West Coast had an average breakfast cost of $7.65. 37. At  0 05. , what is the test value? A) 1.96 B) 1.5 C) –1.5 D) 1.64 Ans: B 38. Give the p-value for the data provided above. A) 0.4987 B) 0.0084 C) 0.1325 D) 0.0668 Ans: D Use the following to answer questions 39-40: The Eagle Ridge Contractors Association claims the average price of a home in their subdivision is $125,150 with a standard deviation of $7,350. A sample of 36 homes for sale in this subdivision had an average selling price of $123,550. Is there evidence that the costs of homes for sale in this subdivision are actually lower than claimed? 39. At 0 05. , what is the test value? A) –1.31 B) 1.31 C) –1.52 D) 1.52 Ans: A 40. What is the p-value for a one-sided test of the data provided above? A) 0.0853 B) 0.0951 C) 0.1327 D) 0.0036 Ans: B 41. When conducting a two-tailed z -test with  0 01. , the test value was 2.07. The decision would be: do not reject the null hypothesis. Ans: True Page 90 Chapter 8 - Hypothesis Testing 42. Alyson Silvastein, a scientist, reports that the average number of hours a person can go without sleep and still function normally is 29 with a standard deviation of five hours. A sample of 49 people had an average of 31 hours that they could go without sleep and still function normally. The test value for this hypothesis would be 2.8. Ans: True 43. The formula for the z-test for a mean is ________. Ans: z X n     44. Dr. Christina Cuttleman, a nutritionist, claims that the average number of calories in a serving of popcorn is 75 with a standard deviation of 7. A sample of 50 servings of popcorn yields an average of 78 calories. Check Dr. Cuttleman's claim at  0 05. . Ans: 0 1: 75 : 75; Critical Values: 1.96; 3.03H H z     Reject 0H . It appears that the average number of calories of popcorn is not 75. 45. At a certain university, the average cost of books per student was $330 per student last semester. In a sample of 50 students this semester, their average cost was $355 with a standard deviation of $85. The Dean of Students believes that the costs are greater this semester. What is the test value for this hypothesis? A) 0.29 B) 0.50 C) 2.08 D) 14.71 Ans: C 46. In a particular city, the average salary of secretaries is $29000 per year. Secretaries at Company A claim that they are paid less than the city average. In a sample of 45 secretaries, their average salary was $25500 per year with a standard deviation of $5000. What is the test value for this hypothesis? A) –4.70 B) –0.70 C) 0.70 D) 4.70 Ans: A 47. An average department store sells 300 men's suits per year. The men's suit departments at a particular national chain of stores claim that they more than the industry average. In a sample of 40 stores, they sold, on the average, 360 suits per year with a standard deviation of $60. What is the test value for this hypothesis? A) 0.16 B) 1.00 C) 3.66 D) 6.32 Ans: D 48. A manufacturer claims that his television will have an average lifetime of at least five years. The standard deviation is seven months. 81 televisions are selected at random, and their average lifetime was found to be 59 months. Is the manufacturer correct? Use  0 025. . Ans: 0 1: 60 : 60; Critical Value: -1.96; 1.29H H z    Do not reject 0H . It appears that the manufacturer's claim is correct and his television will have an average lifetime of at least five years. Page 91 Chapter 8 - Hypothesis Testing 61. Science fiction novels average 200 pages in length. The average length of 14 randomly chosen novels written by I. M. Wordy was 240 pages in length with a standard deviation of 40. Are Wordy's novels significantly longer than the average? Assume α = .05. Ans: The test value is 3.74 and the critical values are  2.1604, so the conclusion is to reject the null hypothesis. 62. The formula for the z -test for proportions is __________. Ans: p̂ p z pq n   63. It has been claimed that at U.C.L.A. at least 40% of the students live on campus. From a sample of 250 students, 90 live on campus. Does the evidence support this claim at  0 01. ? Ans: 0 1: 0.4 : 0.4H p H p  Critical Value: -2.33 1.29z  Do not reject 0H . The claim that at least 40% of the students at U.C.L.A. live on campus is supported by the evidence. 64. A random sample of 450 shoppers at Quincy Mall found that 150 favored longer shopping hours. Is this sufficient evidence to conclude that less than 30% of the shoppers at Quincy Mall favor longer hours? Let  0 05. Ans: 0 1: 0.3 : 0.3H p H p  Critical Value: 1.65 1.54z  Do not reject 0H . The evidence is not sufficient to support the claim that less than 30% of the shoppers favor longer hours. 65. Doctors nationally believe that 70% of a certain type of operation are successful. In a certain hospital, 52 of these operations were observed and 63% of them were successful. If α = .05, is this hospital's success rate different from the national average? A) No, because the test value –0.65 is in the noncritical region. B) Yes, because the test value –0.65 is in the critical region. C) No, because the test value –1.10 is in the noncritical region. D) Yes, because the test value –1.10 is in the noncritical region. Ans: C 66. A political strategist believes that less than 56% of voters in a certain state support a particular issue. He then commisions a poll of 600 voters and 52% of them support this issue. If α = .05, is the political strategist's belief warranted? A) No, because the test value –1.16 is in the critical region. B) No, because the test value –2.17 is in the noncritical region. C) Yes, because the test value –2.17 is in the critical region. D) Yes, because the test value –1.97 is in the critical region. Ans: D Page 94 Chapter 8 - Hypothesis Testing 67. A scientist has a theory that 36% of geese in his area do not fly south for the winter. He tags 75 random geese in the summer and finds that 39% of them do fly south. If α = .05, is the scientist's belief warranted? A) Yes, because the test value –4.51 is in the critical region. B) No, because the test value –4.96 is in the noncritical region. C) Yes, because the test value 4.96 is in the critical region. D) No, because the test value 4.51 is in the critical region. Ans: A 68. One of the assumptions for the chi-square test for a single variance is that the __________ must be normally distributed for the variable under study. Ans: population 69. An assumption of the chi-square test for a single variance is that the observations must be independent of each other. Ans: True 70. A statistician believes that the standard deviation of the weights of firemen is less than 25 pounds. A sample of 20 firemen had a standard deviation of 23.2 pounds. Assume that the variable is normally distributed with  0 05. . What is the critical value? A) 31.410 B) 30.144 C) 10.851 D) 10.117 Ans: B 71. A doctor believes that the standard deviation of systolic blood pressure is 450. A random sample of 24 patients found a standard deviation of 520. Assume the variable is normally distributed and  0 01. . What are the critical values? A) 9.262 and 44.181 C) 13.848 and 36.415 B) 13.091 and 35.172 D) 11.524 and 44.314 Ans: A 72. The critical chi-square value for 20 degrees of freedom for the figure below is 31.410. Ans: True 73. The chi-square critical value for n 16 and  0 01. when the test is left-tailed is 5.812. Ans: False Page 95 Chapter 8 - Hypothesis Testing 74. A lab technician is tested for her consistency by taking multiple measurements of cholesterol levels from the same blood sample. The target accuracy a standard deviation of 1.1 or less. If 16 measurements are taken and their standard deviation is 2.2, is there enough evidence to reject the claim that her standard deviation is within the limit at α = .01? A) Yes, comparing the test value 7.75 and the critical value 5.66. B) No, comparing the test value 30.00 and the critical value 5.53. C) Yes, comparing the test value 7.75 and the critical value 5.53. D) No, comparing the test value 30.00 and the critical value 5.66. Ans: C 75. A lumber mill is tested for consistency by measuring the variance of board thicknesses. The target accuracy a variance of 0.0025 or less. If 26 measurements are taken and their variance is 0.004, is there enough evidence to reject the claim that her standard deviation is within the limit at α = .01? A) No, comparing the test value 40.00 and the critical value 44.31. B) Yes, comparing the test value 8.00 and the critical value 44.31. C) No, comparing the test value 40.00 and the critical value 45.64. D) Yes, comparing the test value 8.00 and the critical value 45.64. Ans: A 76. Assume that in a hypothesis test with null hypothesis 0H : = 17.0 at  0.05, that a value of 19.0 for the sample mean results in the null hypothesis being rejected. That corresponds to a confidence interval result of A) The 0.05% confidence interval for the mean contains the value 19.0 B) The 95% confidence interval for the mean contains the value 19.0 C) The 95% confidence interval for the mean does not contain the value 17.0 D) There is insufficient information as to if the 95% confidence interval for the mean does or does not contain the value 19.0 Ans: C 77. Assume that in a hypothesis test with null hypothesis 0H : = 14.0 at  0.05, that a value of 10.0 for the sample mean results in the null hypothesis to be not rejected. That corresponds to a confidence interval result of A) The 0.05% confidence interval for the mean contains the value 10.0 B) The 95% confidence interval for the mean contains the value 14.0 C) The 95% confidence interval for the mean does not contain the value 14.0 D) There is insufficient information as to if the 95% confidence interval for the mean does or does not contain the value 10.0 Ans: B 78. Assume that a 95% confidence interval for the mean is (11.0, 17.0). Then a hypothesis test of 0H : = 13.0 at   0.05 would result in A) Not rejecting the null hypothesis because 13.0 is less than 17.0 B) Not rejecting the null hypothesis because 13.0 is between 11.0 and 17.0 C) Rejecting the null hypothesis if because 13.0 is more than 11.0 Page 96