Final Exam - Introduction to Statistics - Fall 2008 | STAT 1222, Exams of Statistics

Download Final Exam - Introduction to Statistics - Fall 2008 | STAT 1222 and more Exams Statistics in PDF only on Docsity! STAT 1222 Fall 2008 Common Final Exam December 11, 2008 Please print the following information: Name: Instructor: Student ID #: Section/Time: THIS EXAM HAS TWO PARTS PART I. Consists of 25 multiple choice questions worth a total of 60 points. Read all questions carefully. You may do calculations on the test paper. Mark only one answer; otherwise the answer will be counted as incorrect. In case there is more than one answer, mark the best answer. PART II. This part consists of 3 questions (40 points in total). You MUST show all work for each question in the space provided to receive full credit for that question. If you write your explanations in another part of the test, please indicate accordingly. FOR DEPARTMENTAL USE ONLY: PART II: Questions 1 2 3 Maximum 16 12 12 Score Part I Part II Total STAT1222 Final Exam December 11, 2008 The amounts (in dollars) that 5 randomly selected shoppers spent at Concord Mill Mall are list below: 100 20 0 36 80 1 The mean, median and the standard deviation of the data are. (a) (40.2, 20, 4.50.) (b) (47.2, 36, 1681.33.) (c) (47.2, 36, 41.70.) (d) (51.2, 50, 51.20.) (e) (36.2, 45, 20.70.) Use the following to answer questions 2, 3 and 4. A recent survey revealed that the mean weight of adults in the U.S. was 5.92 ft with a standard deviation of 0.98 ft. 2 If nothing is known about the shape of the distribution of the adult heights, what percentage of adults will be between 3.96 ft and 7.88 ft? (a) At least 75% (b) At most 60% (c) At least 50% (d) At most 40% (e) At most 20% 3 If the distribution of the adult heights in the U.S. can be considered as approximately bell-shaped, then approximately what percentage of adults will be between 3.96 ft and 7.88 ft? (a) 99% (b) 95% (c) 84% (d) 81% (e) 68% 4 The z-score of an adult with A height of 5.50 ft is. (a) z = 2.53 (b) z = 1.51 (c) z = 0 (d) z = -0.25 (e) z = -0.43 STAT1222 page 5 of 13 December 11, 2008 The following is used for questions 12 and 13. In a poll of 764 U.S. citizens taken from 10/17-10/19 by CNN, 49% stated that they would support Barack Obama. Let p denote the proportion of all U.S. citizens who supported Barack Obama. 12. Construct a 95% confidence interval for p. is closest to (a) (0.35 , 0.63) (b) (0.455, 0.524) (c) (248, 500) (d) (0.57, 0.82) (e) (0.40, .58) 13. If no preliminary estimate is available, find the sample size needed to estimate the population proportion p with 95% confidence. The estimate must be accurate within 0.03 of p. (a) n = 800 (b) n = 1010 (c) n = 1068 (d) n = 1547 (e) n = 1987 STAT1222 page 6 of 13 December 11, 2008 The following is used for questions 14, 15 and 16. The following table gives the lifetimes in hours of two batteries for a calculator. We want to test whether the mean lifetimes are different. Battery 1 Battery 2 n1 = 36 n2 = 36 x̄1 = 125.5 x̄2 = 120.7 s1 = 12.5 s2 = 20.6 14. Choose the correct null and alternative hypotheses to test the claim. (a) H0 : µ1 ≥ µ2 versus Ha : µ1 < µ2 (b) H0 : x̄1 ≥ x̄2 versus Ha : x̄1 < x̄2 (c) H0 : µ1 ≤ µ2 versus Ha : µ1 > µ2 (d) H0 : µ1 = µ2 versus Ha : µ1 6= µ2 (e) H0 : µ1 < µ2 versus Ha : µ1 ≥ µ2 15. The value of the standardized test statistic is closest to. (a) 0.52 (b) 0.75 (c) 1.07 (d) 1.20 (e) 2.34 16. Find the p-value for the test and state your conclusion at α = .05. (a) The p-value is 0.0132. The decision: Reject H0 (b) The p-value is 0.2302. The decision: Fail to reject H0 (c) The p-value is 0.1151. The decision: Reject H0 (d) The p-value is 0.1151. The decision: Fail to reject H0 (e) The p-value is 0.8849. The decision: Fail to reject H0 STAT1222 page 7 of 13 December 11, 2008 The following is used for questions 17, 18 and 19. A pharmaceutical company claims that its medicine helps reduce the blood sugar level. Table below shows the blood sugar levels (milligrams per deciliter) of 5 patients before and after taking the medicine. Member 1 2 3 4 5 Before 110 140 150 125 130 After 105 130 135 120 110 The difference in the blood pressures (before− after) for this sample of four patients results in d̄ = 11 and sd = 6.52. Assume that the blood sugar are approximately normally distributed. 17. Does the medicine help reduce the blood sugar level? Choose the appropriate hypothe- ses to test the claim. (a) H0 : µd = 0 versus Ha : µd 6= 0 (b) H0 : d̄ ≤ 0 versus Ha : d̄ > 0 (c) H0 : µd ≤ 0 versus Ha : µd > 0 (d) H0 : µd ≥ 0 versus Ha : µd < 0. (e) H0 : µd < 0 versus Ha : µd ≥ 0. 18. Calculate the value of the standardized test statistic. (a) 3.773 (b) 1.238 (c) 0.816 (d) −1.689 (e) −2.365 19. Find the rejection region and state your decision at α = .05. (a) Rejection Region: t < 2.353; Decision: Reject H0 (b) Rejection Region: t < −3.182; Decision: Reject H0 (c) Rejection Region: t > 2.132; Decision: Reject H0 (d) Rejection Region: t > 3.182; Decision: Fail to reject H0 (e) Rejection Region: t < −2.132; Decision: Fail to reject H0 STAT1222 page 10 of 13 December 11, 2008 The following is used for questions 25. The average hours worked during the year x, and the average hourly tip y, are shown in the table below. Hours 2157 2174 2062 2111 2134 2185 2210 2105 Tips 2.905 2.97 2.35 2.511 2.791 3.04 3.222 2.493 The regression equation is ŷ = 0.0062x− 10.5038. 25. Predict the average hourly tip if the yearly working hour is x = 2200. (a) The predicted amount of tip is $2.56 (b) The predicted amount of tip is $2.61 (c) The predicted amount of tip is $2.81 (d) The predicted amount of tip is $3.14 (e) The average hourly wage cannot be predicted End of Multiple Choice Section STAT1222 page 11 of 13 December 11, 2008 Free Response Questions 1. 5 cars were randomly selected. The weights(in thousand pounds) x and fuel efficiency(MPG) y were measured. The measurements showed that ∑ x = 15.2, ∑ x2 = 48.1, ∑ y = 109, ∑ y2 = 2505, ∑ xy = 316.7. (a). (6 pts.) Calculate the correlation coefficient, r, between the weights and the fuel efficiency of the cars. (b). (5 pts.) Find the regression equation. (c). (5 pts.) Find the standard error of estimate se. STAT1222 page 12 of 13 December 11, 2008 2. The following is the fat content in percentage for 10 dried whole eggs. .62 .55 .34 .24 .80 .68 .76 .65 .30 .40 (a) (4 pts.) Find the five-number summaries, i.e., (Minimum, First Quartile, Second Quartile, Third Quartile, Maximum). (b) (4 pts.) Find the inter-quartile range. (c) (4 pts.) Draw a stem-and-leaf plot.