25 MCQs with Answers Key - Introduction to Statistics | STAT 1222, Exams of Statistics

Download 25 MCQs with Answers Key - Introduction to Statistics | STAT 1222 and more Exams Statistics in PDF only on Docsity! STAT 1222 Spring 2007 Common Final Exam May 3, 2007 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 13 12 15 Score Part I Part II Total STAT1222 Final Exam May 3, 2007 The following is used for questions 1, 2 and 3. Given below are the ages of motorcyclists at the time they were fatally injured in traffic accidents. 17 38 27 14 18 16 21 1 Find the mean of the data. (a) 18.20 (b) 20.58 (c) 21.57 (d) 25.65 (e) 29.32 2 Find the standard deviation of the sample data. (a) 1.25 (b) 3.35 (c) 6.78 (d) 8.38 (e) 10.25 3 Find the median of the data. (a) 17 (b) 18 (c) 20 (d) 22 (e) 24 STAT1222 page 4 of 13 May 3, 2007 10. If one person is randomly selected, what’s the probability that this person does not have hepatitis C? (a) 0.0111 (b) 0.0288 (c) 0.1405 (d) 0.7907 (e) 0.9313 The following is used for questions 11 and 12. For women aged 18-24, the systolic blood pressures (in mm Hg) are normally distributed with a mean of 114.8 and a standard deviation of 13.1. 100 women between the ages of 18 and 24 are randomly selected, let X̄ represent the mean systolic pressure of these 100 women. 11. Find the mean and standard deviation of X̄, i.e., µX̄ , σX̄ . (a) 114.8, 131 (b) 114.8, 13.1 (c) 114.8, 1.31 (d) 11.48, 13.1 (e) 11.48, 1.31 12. What is the probability that the mean systolic blood pressure X̄ is between 112.2 and 116.4? (a) .8649 (b) .3879 (c) .1578 (d) .0571 (e) .0324 STAT1222 page 5 of 13 May 3, 2007 13. A random sample of 21 desktop PCs is selected. The mean life span is 6.8 years with a standard deviation of 2.4 years. Construct a 95% confidence interval for the mean life span of all desktop PCs. Assume that the life spans of all desktop PCs are approxi- mately normally distributed. (a) (5.85, 7.75 ) (b) (1.68, 3.12) (c) (5.60, 8.00) (d) (5.71, 7.89) (e) (5.77, 7.83) 14. Which of the following statements are true about the sampling distribution of x̄? I. The mean of the sampling distribution is equal to the mean of the population. II. The standard deviation of the sampling distribution is equal to the population standard deviation. III. The shape of the sampling distribution is always approximately normal, when n is sufficiently large (n ≥ 30). (a) II only (b) III only (c) I and II only (d) I and III only. (e) None of above. STAT1222 page 6 of 13 May 3, 2007 15. A study of 4200 cell phone users found that 135 of them developed cancer of the brain or nervous system. Construct a 95% confidence interval of the proportion of cell phone users who develop cancer of the brain or nervous system. (a) (0.0175 , 0.0225) (b) (0.0267, 0.0375) (c) (0.190, 0.214) (d) (195 ,209) (e) (0.75 , .85) 16. The following table gives the probability distribution of the number of girls in the families of four children. Number of Girls x P (x) 0 .506 1 .369 2 .102 3 .015 4 .008 Find the mean and the standard deviation of number of the girls. (a) µ =0.23, σ =1.23 (b) µ =0.65, σ =0.786 (c) µ =2.00, σ =1.937 (d) µ =2.35, σ =0.521 (e) µ =3.45, σ =0.281. STAT1222 page 9 of 13 May 3, 2007 The following is used for questions 22, 23 and 24. Among 734 randomly selected Internet users, it was found that 360 of them use the Internet for making travel plans. Use a 0.01 significance level to test the claim that among all Internet users, less than 50% use it for making travel plans. 22. Set up the null and alternative hypotheses to test the claim. (a) H0 : p ≤ 0.50 versus Ha : p > 0.50 (b) H0 : p = 0.76 versus Ha : p 6= 0.76 (c) H0 : p ≥ 0.50 versus Ha : p < 0.50 (d) H0 : p ≥ 367 versus Ha : p < 367 (e) H0 : x̄ ≤ 0.49 versus Ha : x̄ > 0.49 23. Find the P-value for the above mentioned test. (a) 0.0735 (b) 0.3015 (c) 0.4207 (d) 0.4840 (e) 0.7054 24. At the significance level of 0.01, your conclusion is. (a) Accept H0 since P-value is less than 0.01 (b) Fail to accept H0 correct since P-value is greater than 0.01 (c) Accept H0 since P-value is greater than 0.01 (d) Fail to accept H0 since P-value is less than 0.01 (e) None of above STAT1222 page 10 of 13 May 3, 2007 The following is used for questions 25. The following table gives the car weight,x (in lb) and the fuel consumption, y (in miles/gal) for 7 randomly selected cars. Weight 3175 3450 3225 3985 2440 2500 2290 MPG 27 29 27 24 37 34 37 The regression equation is ŷ = −0.00797x + 54.7. 25. Predict the fuel consumption in MPG if the car weight is x = 3000 lb. (a) The MPG is 25.16 (b) The MPG is 28.51 (c) The MPG is 30.79 (d) The MPG is 35.22 (e) The MPG cannot be predicted End of Multiple Choice Section STAT1222 page 11 of 13 May 3, 2007 1. 10 people were randomly selected, and their systolic (x) and diastolic (y) blood pressures were measured. Systolic 138 130 135 140 120 125 120 130 130 144 Diastolic 82 91 100 100 80 90 80 80 80 98 From the data, we have: ∑ x = 1312, ∑ x2 = 172730, ∑ y = 881, ∑ y2 = 78309, ∑ xy = 116008. (a). (6 pts.) Calculate the correlation coefficient, r, between the systolic and dias- tolic blood pressures. (b). (5 pts.) Find the equation of the regression line. (c). (5 pts.) Use the equation in part (c) to predict y when x = 128.