CH10 T
76. Which of the following is a test statistic used to test a hypothesis about a population parameter?
A) B) C) D) z Answer: D
75. What is the probability of making a Type II error if the null hypothesis is actually true?
A) B) 1 C) 0 D) 0.05 Answer: C
145. Which of the following is the alternate hypothesis?
A) $20,000 B) $20,000 C) $20,000 D) = $20,000 E) = $20,000 Answer: B
115. What is the critical z-value for this test?
A) + 1.96 B) - 1.96 C) + 1.65 D) - 1.65 Answer: C
86. What does z equal for an = 0.01 and a left tail test?
A) +2.33 B) -2.33 C) +2.58 D) -2.58 Answer: B
150. If = 0.05, what is the critical t value?
A) - 2.365 B) 1.96 C) 2.365 D) 2.447 E) - 2.447 Answer: D
135. What is the critical value if the level of significance is 0.10?
A) -1.282 B) 1.65 C) -2.58 D) 2.58 Answer: B
88. If = 0.05, what is the probability of making a Type I error?
A) 0 B) 1/20 C) 19/20 D) 20/20 Answer: B
117. What is the p-value for this test?
A) 0.0000 B) 0.0124 C) 0.0500 D) 0.4938 Answer: A
141. What is the z-statistic?
A) 0.025 B) 0.278 C) -1.65 D) 1.67 Answer: D
142. What is the p-value?
A) 0.025 0 B) 0.4525 C) 0.0475 D) 0.0500 Answer: C
77. If = 0.05 for a two-tailed test, how large is the acceptance area?
A) 0.050 B) 0.025 C) 0.950 D) 0.975 Answer: C
Use the following to answer questions 137-143: It is claimed that in a bushel of peaches less than ten percent are defective. A sample of 400 peaches is examined and 50 are found to be defective. 137. What is the null hypothesis?
A) 0.10 B) 0.10 C) 0.10 D) < 0.10 E) = 0.10 Answer: B
140. What is the sample proportion?
A) 0.10 B) 0.125 C) 40 D) 0.40 Answer: B
138. What is the alternate hypothesis for a one-sided test?
A) 0.10 B) > 0.10 C) 0.10 D) = 0.10 E) < 0.10 Answer: E
85. If 20 out of 50 students sampled live in a college dormitory, what is the estimated proportion of students at the University living in a dormitory?
A) 0.20 B) 0.40 C) 0.50 D) 0.60 Answer: B
134. What is the p-value?
A) 0.3461 B) 0.1539 C) 0.3078 D) 0.0100 Answer: B
131. What is the sample proportion?
A) 0.41 B) 0.36% C) 0.41% D) 0.36 Answer: D
133. What is the z-statistic?
A) 1.02 B) 1.22 C) -1.02 D) -1.22 Answer: C
153. What is the sample standard deviation?
A) 1.177 B) 6.6 C) 1.385 D) 7.6 Answer: A
152. What is the sample variance?
A) 1.177 B) 6.6 C) 1.385 D) 7.6 Answer: C
146. If the level of significance is 0.10, what is the critical value?
A) 1.65 B) 2.58 C) 1.28 D) 1.28 E) 1.65 Answer: E
139. What is the critical value for = 0.025?
A) 1.96 B) 1.65 C) - 1.96 D) -1.65 Answer: C
132. What is the critical value if = 0.01?
A) 2.58 B) 2.33 C) 2.58 D) -2.33 Answer: C
80. If the critical z-value for a test statistic equals 2.45, what value of the test statistic would guarantee no chance of making a Type I error?
A) 3.74 B) 10,000 C) 2.46 D) 4.56 Answer: B
151. What is the sample mean?
A) 6.6 B) 7.6 C) 1.177 D) 2.447 Answer: B
149. What is the degrees of freedom?
A) 7 B) 8 C) 6 D) 6.6 E) 7.6 Answer: C
63. A machine is set to fill the small size packages of M&M candies with 56 candies per bag. A sample revealed: 3 bags of 56, 2 bags of 57, 1 bag of 55, and 2 bags of 58. How many degrees of freedom are there?
A) 9 B) 1 C) 8 D) 7 Answer: D
81. For a one-tailed hypothesis test, the critical z-value of the test statistic is -2.33. Which of the following is true about the hypothesis test?
A) = 0.05 for a lower-tailed test B) = 0.01 for a lower-tailed test C) = 0.05 for an upper-tailed test D) = 0.01 for an upper-tailed test Answer: B
Use the following to answer questions 129-136: Based on the Nielsen ratings, the local CBS affiliate claims its 11:00 PM newscast reaches 41% of the viewing audience in the area. In a survey of 100 viewers, 36% indicated that they watch the late evening news on this local CBS station. 129. What is the null hypothesis?
A) = 0.36 B) = 0.41 C) 0.36 D) = 0.41 Answer: B
130. What is the alternate hypothesis?
A) = 0.36 B) = 0.41 C) 0.41 D) 0.41 Answer: C
Use the following to answer questions 147-155: The mean weight of newborn infants at a community hospital is 6.6 pounds. A sample of seven infants is randomly selected and their weights at birth are recorded as 9.0, 7.3, 6.0, 8.8, 6.8, 8.4, and 6.6 pounds. 147. The null hypothesis is
A) = 6.6 B) 6.6 C) 6.6 D) > 7.6 E) 7.6 Answer: A
148. What is the alternate hypothesis?
A) = 6.6 B) 6.6 C) 6.6 D) > 7.6 E) 7.6 Answer: B
70. What are the two rejection areas in using a two-tailed test and the 0.01 level of significance when n is large and the population standard deviation is known?
A) Above 1.96 and below -1.96 B) Above 1.65 and below -1.65 C) Above 2.58 and below -2.58 D) Above 1.00 and below -1.00 Answer: C
68. What is a Type II error?
A) Accepting a false null hypothesis B) Rejecting a false null hypothesis C) Accepting a false alternate hypothesis D) Rejecting a false alternate hypothesis Answer: A
73. For a two-tailed test at the 0.05 significance level, what is the rejection region when n if large and the population standard deviation is known?
A) Between 1.96 B) Between 1.65 C) Greater than +1.96 and less than - 1.96 D) Greater than +1.65 and less than -1.65 Answer: C
69. If the alternate hypothesis states that does not equal 4,000, what is the rejection region for the hypothesis test?
A) Both tails B) Lower or left tail C) Upper or right tail D) Center Answer: A
78. If the alternative hypothesis states that > 6,700, what is the rejection region for the hypothesis test?
A) Both tails B) Lower tail C) Upper tail D) Center Answer: C
54. Which of the following does NOT hold true for the t distribution?
A) Confidence intervals will be wider than for large samples. B) The region of acceptance will be larger than for large samples. C) A larger computed t value will be needed to reject the null hypothesis than for large samples using z. D) There is only one t distribution. Answer: D
84. A manufacturer of stereo equipment introduces new models in the fall. Retail dealers are surveyed immediately after the Christmas selling season regarding their stock on hand of each piece of equipment. It has been discovered that unless 40% of the new equipment ordered by the retailers in the fall had been sold by Christmas, immediate production cutbacks are needed. The manufacturer has found that contacting all of the dealers after Christmas by mail is frustrating as many of them never respond. This year 80 dealers were selected at random and telephoned regarding a new receiver. It was discovered that 38% of those receivers had been sold. Since 38% is less than 40%, does this mean that immediate production cutbacks are needed or can this difference of 2 percentage points be attributed to sampling? Test at the 0.05 level. Computed z = -0.37.
A) Cut back production B) Do not cut back production C) Cannot determine based on information given D) None of the above Answer: B
67. What do we call the statement that determines if the null hypothesis is rejected?
A) Decision rule B) Test statistic C) Alternate hypothesis D) Critical value Answer: A
89. The claim that "40% of those persons who retired from an industrial job before the age of 60 would return to work if a suitable job was available," is to be investigated at the 0.02 level of risk. If 74 out of the 200 workers sampled said they would return to work, what is our decision?
A) Do no reject the null hypothesis because -0.866 lies in the region between 0 and -2.33 B) Do not reject the null hypothesis because -0.866 lies in the region between 0 and -2.58 C) Reject the null hypothesis because 37% is less than 40% D) Do not reject the null hypothesis because 37% lies in the area between 0% and 40% Answer: A
71. If the 1% level of significance is used and the computed value of z is +6.00, what is our decision?
A) Do not reject H0 B) Reject H0 C) Reject H1 D) None of the above Answer: B
57. Test at the 0.01 level the statement that 55% of those families who plan to purchase a vacation residence in Florida want a condominium. The null hypothesis is = 0.55 and the alternate is 0.55. A random sample of 400 families who planned to buy a vacation residence revealed that 228 families want a condominium. What decision should be made regarding the null hypothesis?
A) Do not reject it B) Reject it C) Cannot accept nor reject it based on the information given D) None of the above Answer: A
62. A manufacturer wants to increase the absorption capacity of a sponge. Based on past data, the average sponge could absorb 3.5 ounces. After the redesign, the absorption amounts of a sample of sponges were (in ounces): 4.1, 3.7, 3.3, 3.5, 3.8, 3.9, 3.6, 3.8, 4.0, and 3.9. What is the decision rule at the 0.01 level of significance to test if the new design increased the absorption amount of the sponge?
A) Do not reject null hypothesis if computed t is less than 2.580 B) Do not reject null hypothesis if computed t is less than 2.821 C) Reject null hypothesis if computed z is 1.96 or larger D) Reject null hypothesis if computed t is less than 2.764 Answer: B
60. From past records it is known that the average life of a battery used in a digital clock is 305 days. The battery life is normally distributed. The battery was recently modified to last longer. A sample of 20 of the modified batteries was tested. It was discovered that the mean life was 311 days and the sample standard deviation was 12 days. We want to test at the 0.05 level of significance whether the modification increases the life of the battery. What is our decision rule?
A) Do not reject the null hypothesis if computed t is 1.96 or greater B) Reject the null hypothesis if computed t is less than 1.96 C) Do not reject the null hypothesis if computed t is 1.729 or greater D) Reject the null hypothesis if computed t is 2.086 or greater E) None of the above Answer: E
Use the following to answer questions 144-146: The mean gross annual incomes of certified welders are normally distributed with the mean of $20,000 and a standard deviation of $2,000. The ship building association wishes to find out whether their welders earn more or less than $20,000 annually. The alternate hypothesis is that the mean is not $20,000. 144. If the level of significance is 0.10, what is the decision rule?
A) Do not reject the null hypothesis if computed z lies between -1.65 and +1.65; otherwise, reject it B) Do not reject the null hypothesis if computed z is greater than 1.65; otherwise, reject it C) Do not reject the null hypothesis if computed z lies between -1.96 and +1.96; otherwise, reject it D) Reject the null hypothesis if computed z is below -1.96; otherwise, reject it Answer: A
118. Based on the computed test statistic or p-value, what is our decision about the average cost?
A) Equal to $8,500 B) Greater than $8,500 C) Less than $8,500 D) Not equal to $8,500 Answer: B
87. What do tests of proportions require of both n and n(1 - )?
A) Exceed 30 B) Exceed 5 C) Exceed 100 D) Be equal Answer: B
143. If = 0.025, what will be the decision?
A) Fail to reject the null and conclude the defects are not greater than 10% B) Reject the null and conclude the defects are not greater than 10% C) Reject the null and conclude the defects are greater than 10% D) Fail to reject the null and conclude the defects are not less than 10% Answer: D
154. What is the decision for a statistical significant change in average weights at birth at the 5% level of significance?
A) Fail to reject the null hypothesis and conclude the mean is 6.6 lb. B) Reject the null hypothesis and conclude the mean is higher than 6.6 lb. C) Reject the null hypothesis and conclude the mean is lower than 6.6 lb. D) Cannot calculate because population standard deviation is unknown. Answer: A
155. What is the decision for a significant increase in the average birthrate at a 5% level of significance?
A) Fail to reject the null hypothesis and conclude the mean is 6.6 lb. B) Reject the null hypothesis and conclude the mean is lower than 6.6 lb. C) Reject the null hypothesis and conclude the mean is greater than 6.6 lb. D) Cannot calculate because population standard deviation is unknown. Answer: C
136. What is your decision if = 0.01?
A) Fail to reject the null hypothesis and conclude the newscast reaches about 41% of the audience. B) Reject the null hypothesis and conclude the newscast does not reach 41% of the audience. C) Fail to reject the alternate and conclude the newscast does not reach 41% of the audience. D) Reject the alternate and conclude the newscast reaches about 41% of the audience. Answer: A
83. Which of the following is NOT one of the five steps in the hypothesis testing procedure?
A) Formulate a decision rule B) State the null and alternate hypotheses C) Select a level for D) Identify the test statistic E) All of the above are part of the five steps Answer: C
72. What is another name for the alternate hypothesis?
A) Null hypothesis B) Hypothesis of no difference C) Rejected hypothesis D) Research hypothesis Answer: D
82. If we reject the null hypothesis what can we conclude subject to the risk?
A) Null hypothesis is false B) Alternative hypothesis is false C) Null hypothesis is true D) Both the null hypothesis and the alternative hypothesis are true E) Both the null hypothesis and the alternative hypothesis are false Answer: A
Use the following to answer questions 114-118: The average cost of tuition, room and board at small private liberal arts colleges is reported to be $8,500 per term, but a financial administrator believes that the average cost is higher. A study conducted using 350 small liberal arts colleges showed that the average cost per term is $8,745 with a standard deviation of $1,200. Let = 0.05. 114. What is the null and alternative hypotheses for this study?
A) Null: $9,000; alternative: > $9,000 B) Null: $9,000; alternative: < $9,000 C) Null: $8,500; alternative: > $8,500 D) Null: $8,500; alternative: < $8,500 Answer: C
55. What value does the null hypothesis make a claim about?
A) Population parameter B) Sample statistic C) Sample mean D) Type II error Answer: A
58. What is the level of significance?
A) Probability of a Type II error B) Probability of a Type I error C) z-value of 1.96 D) Beta error Answer: B
90. In hypothesis testing, what is the level of significance?
A) Risk of rejecting the null hypothesis when it is true B) Symbolized by the Greek letter " " C) Value between 0 and 1 D) Selected before a decision rule can be formulated E) All of the above are true Answer: E
64. A random sample of size 15 is selected from a normal population. The population standard deviation is unknown. Assume that a two-tailed test at the 0.10 significance level is to be used. For what value of t will the null hypothesis not be rejected?
A) To the left of -1.282 or to the right of 1.282 B) To the left of -1.345 or to the right of 1.345 C) To the left of -1.761 or to the right of 1.761 D) To the left of -1.645 or to the right of 1.645 Answer: C
61. A manufacturer wants to increase the shelf life of a line of cake mixes. Past records indicate that the average shelf life of the mix is 216 days. After a revised mix has been developed, a sample of nine boxes of cake mix gave these shelf lives (in days): 215, 217, 218, 219, 216, 217, 217, 218 and 218. At the 0.025 level, has the shelf life of the cake mix increased?
A) Yes, because computed t is greater than the critical value. B) Yes, because computed t is less than the critical value. C) No, because computed t lies in the region of acceptance. D) No, because 217.24 is quite close to 216. Answer: A
59. The mean length of a small counter balance bar is 43 millimeters. There is concern that the adjustments of the machine producing the bars have changed. Test the claim at the 0.02 level that there has been no change in the mean length. The alternate hypothesis is that there has been a change. Twelve bars (n = 12) were selected at random and their lengths recorded. The lengths are (in millimeters) 42, 39, 42, 45, 43, 40, 39, 41, 40, 42, 43 and 42. The mean of the sample is 41.5 and the standard deviation 1.784. Computed t = - 2.913. Has there been a statistically significant change in the mean length of the bars?
A) Yes, because the computed t lies in the area beyond the critical. B) No, because the information given is not complete. C) No, because the computed t lies in the area to the right of -2.718. D) None of the above Answer: A
56. A p-value can be computed for
A) a hypothesis test about a population mean B) a hypothesis test about a population proportion. C) a hypothesis test about a population mean based on a sample size of 10. D) A, B, and C Answer: A
66. To conduct a test of hypothesis with a small sample, we need to be able to make the following assumption that:
A) a larger computed value of t will be needed to reject the null hypothesis B) the region of acceptance will be wider than for large samples C) the confidence interval will be wider than for large samples D) the population is normally distributed. Answer: D
92. What is the sample proportion defined as?
A) n B) x/n C) n! D) Answer: B
74. The sample size and the population proportion are respectively represented by what symbols?
A) p and n B) C) z and t D) n and Answer: D
91. Which symbol represents a population proportion?
A) pc B) z C) D) Answer: D
79. What are the critical z-values for a two-tailed hypothesis test if = 0.01?
A) ± 1.96 B) ± 2.33 C) ± 2.58 D) ± 1.65 Answer: C
116. What is the test statistic for this test?
A) ±3.82 B) 0.204 C) -3.82 D) +3.82 Answer: D
65. What is the critical value for a one-tailed hypothesis test in which a null hypothesis is tested at the 5% level of significance based on a sample
size of 25? A) 1.708 B) 1.711 C) 2.060 D) 2.064 Answer: B