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Statistics 13C Spring 2009 Midterm 2 Name___________________________________ Student ID___________________________________ Section___________________________________ Instruction: You have 50 minutes to work on this exam. It is closed book and one page of formula is provided with the exam. You may use your hand held calculator. The exam has 16 multiple choice problems. Please, hand in BOTH the marked hardcopy and scantron form. You need to mark your answers in BOTH. A blank hardcopy is NOT acceptable. This is version A. Please mark the corresponding circle on scantron. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) The sample size needed to estimate a population mean within 1.5 units with a 95% confidence when the population standard deviation equals 10 is A) 121 B) 13 C) 171 D) 54 2) From a sample of 200 items, 12 items are defective. The point estimate of the population proportion defective will be: A) 12 B) 0.06 C) 16.67 D) 0.12 3) Suppose a large labor union wishes to estimate the mean number of hours per month a union member is absent from work. The union decides to sample 402 of its members at random and monitor the working time of each of them for 1 month. At the end of the month, the total number of hours absent from work is recorded for each employee. Which of the following should be used to estimate the parameter of interest for this problem? A) A large sample confidence interval for p. B) A large sample confidence interval for μ. C) A small sample confidence interval for μ. D) A small sample confidence interval for p 4) You are interested in purchasing a new car. One of the many points you wish to consider is the resale value of the car after 5 years. Since you are particularly interested in a certain foreign sedan, you decide to estimate the resale value of this car with a 98% confidence interval. You manage to obtain data on 17 recently resold 5-year-old foreign sedans of the same model. These 17 cars were resold at an average price of $12,390 with a standard deviation of $600. Suppose that the interval is calculated to be How could we alter the sample size and the confidence coefficient in order to guarantee a decrease in the width of the interval? A) Increase the sample size but decrease the confidence coefficient. B) Decrease the sample size but increase the confidence coefficient. C) Increase the sample size and increase the confidence coefficient. D) Keep the sample size the same but increase the confidence coefficient. 5) The director of a hospital wishes to estimate the mean number of people who are admitted to the emergency room during a period. The director randomly selects 49 different periods and determines the number of admissions for each. For this sample, x =12.3 and s=5. Estimate the mean number of admissions per period with a 95% confidence interval. A) 12.3 ± 0.876 B) 12.3 ± 1.4 C) 12.3 ± 0.254 D) 12.3 ± 8.23 6) If a hypothesis test were conducted using α = 0.01, to which of the following p-values would cause the null hypothesis to be rejected. A) 0.015 B) 0.001 C) 0.060 D) 0.020 7) The business college computing center wants to determine the proportion of business students who have laptop computers. If the proportion exceeds 35%, then the lab will scale back a proposed enlargement of its facilities. Suppose 250 business students were randomly sampled and 65 have laptops. We are interested in testing the null hypothesis that the proportion is at most 35%. Which of the following statements is incorrect? A) The sample size n satisfies n ≥ 30. B) The test statistic is -2.98 C) The distribution of the test statistic is approximately normal. D) At 1% the rejection region is Z< -2.33 8) A quality control officer tests bottles of shampoo to see if the filling machines are putting the proper amount in each bottle. They do not want to shut down production unless there is strong evidence indicating that the machines are not functioning properly. After testing a sample of bottles, the quality control officer decides to leave the filling machines operating. Actually, however, the filling machines are not operating properly. Which type of error, if any, did the quality control officer commit? A) This is a Type I error. B) This is a Type II error. C) This is a correct decision. D) Need more information to answer this question. 9) If we reject the null hypothesis, we conclude that A) There is not enough statistical evidence to infer that the alternative hypothesis is true B) There is enough statistical evidence to infer that the alternative hypothesis is true C) There is enough statistical evidence to infer that the null hypothesis is true D) The test is statistically insignificant at whatever level of significance the test was conducted at H : 75 versus H a : 75 10) In testing the hypotheses 0 , the following information is known: n = 64, x = 78, and = 10. The test statistic is equal to: A) +1.96 B) +2.4 C) -2.4 D) –1.96 H 0 : 50 11) Suppose that a t-test is being conducted at the 0.05 level of significance to test versus H1 : 50 . A sample of size 20 is randomly selected. The rejection region is: A) t > 1.725 B) t < -1.729 C) t > -2.093 D) t < 2.086 12) Salary data were collected from 21 CEOs in the consumer product industry and 21 CEOs in the telecommunication industry. The data were analyzed in order to compare mean salaries of CEOs in the two industries. What of the following assumptions is necessary to perform the test described above? A. The standard deviations of the two populations of salaries are both large B. The means of the two populations of salaries are equal C. The population of salaries for each of the two industries has an approximately normal distribution D. The sample sizes are equal. 13) In a controlled laboratory environment, a random sample of 10 adults and a random sample of 10 children were tested by a psychologist to determine the room temperature that each person finds most comfortable. The data are summarized below: Suppose that the psychologist decides to construct a 99% confidence interval for the difference in mean comfortable room temperatures instead of proceeding with a test of hypothesis. The 99% confidence interval turns out to be (-2.9, 3.1). Select the correct statement. A. It can be concluded at the 99% confidence level that the true mean room temperature for adults exceeds that for children. B. It can be concluded at the 99% confidence level that the true mean comfortable room temperature for children exceeds that for adults. C. It cannot be concluded at the 99% confidence level that there is actually a difference between the true mean comfortable room temperatures for the two groups. D. It can be concluded at the 99% confidence level that the true mean comfortable room temperature is between -2.9 and 3.1. 14) In a controlled laboratory environment, a random sample of 10 adults and a random sample of 10 children were tested by a psychologist to determine the room temperature that each person finds most comfortable. The data are summarized below: If the psychologist wished to test the hypothesis that children prefer warmer room temperatures than adults, which set of hypotheses would he use? A. : ( - ) = 0 vs. Ha( - ) ≠ 0 B. : ( - ) = 0 vs. Ha: ( - ) < 0 C. : ( - ) = 0 vs. Ha: ( - ) > 0 D. : ( - ) = 3 vs. Ha: ( - ) ≠ 0 15) A researcher is investigating which of two newly developed automobile engine oils is better at prolonging the life of an engine. Since there are a variety of automobile engines, 20 different engine types were randomly selected and were tested using each of the two engine oils. The number of hours of continuous use before engine breakdown was recorded for each engine oil. Based on the information provided, what type of analysis will yield the most useful information? A. Matched pairs comparison of population means. B. Independent samples comparison of population proportions. C. Independent samples comparison of population means. D. Matched pairs comparison of population proportions. 16) Two samples of sizes 15 and 20 are randomly and independently selected from two normally distributed populations, where the unknown population variances are assumed to be equal. The number of degrees of freedom associated with the two-sample t-test is: A. 19 B. 33 C. 35 D. 34