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

Download Common Final Exam - Introduction to Statistics | STAT 1222 and more Exams Statistics in PDF only on Docsity! STAT 1222 SPRING 2006 Common Final Exam May 4, 2006 Please print the following information: Name: Instructor: Student ID #: Section/Time: THIS EXAM HAS TWO PARTS PART I. Consists of 30 multiple choice questions worth a total of 60 points. Read all questions carefully. You may do calculations on the test paper. Mark the number of the opscan sheet corresponding to the test question number with a Number 2 pencil or a mechanical pencil with HB lead. Mark only one answer; otherwise the answer will be counted as incorrect. In case there is more than one answer, mark the best answer. Please make sure that your name appears on the opscan sheet in the spaces provided. 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. At the end of the examination, you MUST hand in this test booklet, your answer sheet and all scratch paper. FOR DEPARTMENTAL USE ONLY: PART II: Questions 1 2 3 Maximum 14 14 12 Score Part I Part II Total STAT1222 Final Exam May 4, 2006 The following is used for questions 1, 2 and 3. A sample of eight resistors of a certain type resulted in the following sample resistances (ohms): 40, 43, 39, 35, 37, 43, 46, 37 1 Find the median of the sample. (a) 36 (b) 37.5 (c) 39.5 (d) 38.5 (e) 43 2 Find the standard deviation of the sample. (a) 14 (b) 98 (c) 12.25 (d) 3.742 (e) 3.5 3 Find the first quartile of the sample. (a) 35 (b) 39 (c) 43 (d) 37 (e) 40 STAT1222 page 4 of 15 May 4, 2006 10. 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 divided by square root of the sample size. III. The shape of the sampling distribution is always approximately normal. (a) I only (b) II only (c) III only (d) I and II only (e) I and III only. The following is used for questions 11 and 12. Scores for men on the verbal portion of the SAT-I test are normally distributed with a mean of 509 and a standard deviation of 108. A random sample of 36 men is selected. 11. Identify the mean and standard error of their sample mean score, (µx̄, σx̄) (a) 509, 108 (b) 509, 18 (c) 84.833, 108 (d) 509, 3 (e) 14.139, 3 12. What is the probability that their sample mean score x̄ is greater than 540? (a) .9573 (b) .5427 (c) .6554 (d) .0427 (e) .17 STAT1222 page 5 of 15 May 4, 2006 13. Suppose you want to obtain an estimate of the mean caffeine content in a cup of coffee correct to within 3 mg and with 80 % confidence. Find the minimum sample size necessary to estimate the mean caffeine content in a cup of coffee. Assume that the population is normally distributed with a standard deviation of 30. (a) n = 271 (b) n = 3855 (c) n = 164 (d) n = 664 (e) n = 2401. The following is used for questions 14 and 15. A random sample of elementary school children in New York state is to be selected to estimate the proportion p who have received a medical examination during the past year. A random sample of 200 elementary school children indicated that 18 of them had received a medical examination in the past year. 14. Find point estimate for p and also construct a 95% confidence interval for p. (a) .09, (.04 , .14) (b) .9, (.01, .17) (c) 200, (.01, .17) (d) 200, (.05 , .13) (e) .09, (.05 , .13). 15. Using the information from the above sample, find the minimum sample size needed to estimate the population proportion p with 99% confidence. The estimate must be accurate to within .02 of p. (a) n = 1701 (b) n = 4145 (c) n = 1358 (d) n = 2936 (e) n = 2401. STAT1222 page 6 of 15 May 4, 2006 The following is used for question 16. Starting salaries of 50 college graduates who have taken a statistics course has a mean of $42,786 and a standard deviation of $8,912. 16. Construct a 97% confidence interval for the mean starting salary. Also, report the critical value zc corresponding to a confidence level of c = .97. (a) (40051.05, 45520.95), 2.17 (b) (38257.15, 44512.85), 2.17 (c) (40315.72, 45256.28), 1.96 (d) (40164.48,45407.52), 2.08 (e) (38146.26,46128.74), 2.08 17. In the context of statistical hypothesis testing, a Type I error is: (a) Failing to reject the null hypothesis when it is false (b) Failing to reject the alternative hypothesis when it is false (c) Rejecting the null hypothesis when it is true (d) Failing to reject the alternative hypothesis when it is true (e) All of the above STAT1222 page 9 of 15 May 4, 2006 The following is used for questions 24, 25 and 26. Let x denote the number of potential weapons detected by a metal detector at an airport on a given day. The probability distribution of x is x P (x) 0 .14 1 .28 2 .22 3 .18 4 .12 5 .06 24. What is the probability that at least 3 potential weapons are detected? (a) .18 (b) .30 (c) .12 (d) .36 (e) .06. 25. Find the mean number of potential weapons detected. (a) 2.04 (b) 3 (c) 2.5 (d) 3.12 (e) 2.16. 26. What is the variance of the random variable, x? (a) .12 (b) 1.126 (c) 2.038 (d) 1.56 (e) .752. STAT1222 page 10 of 15 May 4, 2006 The following is used for questions 27, 28 and 29. Golf-course designers have become concerned that old courses are becoming obsolete since new technology has given golfers the ability to hit the ball so far. Designers, therefore, have proposed that new golf courses need to be built expecting that the average golfer can hit the ball more than 230 yards on average. A random sample of 177 golfers show that their mean driving distance is 230.7 yards, with a standard deviation of 41.8. 27. Set up the null and alternative hypotheses to test for the designers belief. (a) H0 : µ ≤ 230.7 versus Ha : µ > 230.7 (b) H0 : µ = 230.7 versus Ha : µ 6= 230.7 (c) H0 : µ ≥ 230.7 versus Ha : µ < 230.7 (d) H0 : µ ≤ 230 versus Ha : µ > 230 (e) H0 : µ ≥ 230 versus Ha : µ < 230 28. Find the value of the standardized test statistic. (a) .7 (b) .223 (c) .125 (d) -.7 (e) -.125 29. Find the P-value for the above mentioned test. (a) .0871 (b) .5871 (c) .0228 (d) .9772 (e) .4129 STAT1222 page 11 of 15 May 4, 2006 The following is used for question 30. The equation of the best fit line relating the amount of bill (in dollars) x to the amount of tip (in dollars) y is ŷ = .18x− 2.70 30. Predict the amount of tip if the amount of bill is $ 70. (a) The predicted amount of tip is $12.60 (b) The predicted amount of tip is $ 10.50 (c) The predicted amount of tip is $ 9.90 (d) The predicted amount of tip is $14 End of Multiple Choice Section STAT1222 page 14 of 15 May 4, 2006 (b) (5 pts.) Find the standardized test statistic. (c) (3 pts.) State the rejection region at α = .01 (d) (3 pts.) At α = .01, does the data support the company’s claim? Why or why not? STAT1222 page 15 of 15 May 4, 2006 3. At a trade show, a random sample of n = 50 attendees were interviewed. Out of the 50 attendees who were interviewed, 30 said they were more likely to visit an exhibit when there is a giveaway. At α = .03, test the claim that more than 52% of the attendees at trade shows were more likely to visit an exhibit when there is a giveaway. (a) (2 pts.) State the null and the alternative hypotheses. H0 : Ha : (b) (5 pts.) Find the value of the standardized test statistic based on the observed sample. (c) (5 pts.) Find the critical value(s) at level α = .03 and state the rejection rule. What is your decision?