STAT 201 Final, Fall 2000

AMERICAN UNIVERSITY OF BEIRUT MATHEMATICS 207, FINAL EXAMINATION February 2. 2001 Fall ovo-o| Time = 1 hour 30 mimutes Aids Allowed: You are allowed to use one formula sheet, a calculator, Standard Normal table. and Student-t table. INSTRUCTIONS: Please, PRINT vour name aud [D number on both the booklet and question/answer sheet. Use the question sheet to answer the multiple choice part while the booklet is to auswer the written questions and rough work. Checking more than one answer for the multiple choice question will give vou NO points for that particular question. However, this can be corrected by adding the sentence “My answer is —". At the end, inchide vour question sheet: in vour booklet before you hand in your exam. (GOOD LUCK!) Part I: Multiple Choice (Each question carries 5 points) 1. A researcher divided subjects into two groups according to gender and then randomly selected members from each group for her sample. What sampling technique was the researcher using? (a) Cluster (b) systematic (c) stratified (d) simple random sampling (e} none of the above 2. When data are categorized as. for example. place of residence (rural, siburban, arbau). tle most appropriate measnre of central tendency is (a) mean (b) median (ce) mode (d} mid-range (@) none of the above . When a distribution is bell shaped, approximately . What percentage of uw data values will fall within one standard deviation of the mean? (a) 68% (b) 90% (c) 95% (d) 99% (e) none of the above Over —» 4. According to the Burean of Labor Statistics the meau telephone ex- peuditure per customer unit was $690 in 1994. We want to perform a hypothesis test to decide whether last year’s mean expenditure has increased over the 1994 mean of 5690. The null aud alternative hy- potheses are: Hy: pe = 5690 VS Hy: pe > S690, where je is last vear’s mean telephone expenditure per consumer unit. Suppose the result of carrying out the hypothesis test lead to non- rejection of the ull hypothesis. If in fact that last vear’s mean tele- phone expenditure per consumer unit was greater than 1994 mean of 8690. then the corchision of uot rejecting Af, may be classified as (a) type L error (b) type TL error (c) correct decision (d) Can't tell from the above information A scale used in analytical chemistry gives weiglits in repeated weighing of the same object. that have normal distribution with mean equal to the true weight of the object. The standard deviation of repeated measurements is known to be ¢ = 0.10 g. If the student wants to estimate the true weight within +£0.01 ¢. with 95% confidence . How many weighines should she average to achieve this? (a) 350 (b) 385 {c) 400 (d)1350 (e) none of the above ‘Lhe scores of forr roommates of the School Aptitude Test (SAT) have mean # = 589 and standard deviation s=37. Assume that those scoves coustitite a raudom sample from the pool of all scores of students who have taken the SAT exam. Purther, assume that the scores follow a normal distribution with unknown mean p. Then a 90% confidence interval for js is (a) (565,26. 612.7 1) (b) (552.00, 626.00) (c) (545.47, 632.53) (A) (552.74. 625.26) (e) Can't be determined from the above information. 7. Let sl and B be eveurs such that P(A) = 1/3. P(4l or B) = 1/2. and P(AGB) = 1/10. Pind PCB) (a) 4/15 (b) 8/15 (c) 11/15 (d) 14/15 (e) uone of the above Part IL: Written questions (Please, slow all work!) 1. Given the following data points: (a) Find the regression equation for the above data points. (10 pts) (b) Luterpret the meaning of the regression liue as the ” best linear fit” for the above data points. (5 pts) (c) Obtain R?. the coefficient of determination. (5 pts) 2. A factory manaver collected data on the miumber of equipment break- downs per day, From those data, she derived the probability distribu- tion shown in the table below, where WV denotes the number of break- downs in a given day w {| 8 1 P(Wew) [O80 0.150 2 0A (a) Determine jay and oy. (6 pts) (b) Ou the average, how many breakdowns occur per day? (4 pts) (c) Abont Low many breakdowns are expected diriug one-vear pe- riod. assnine 250 workin days pet vear? {5 pts)