Solutions to Exam 1 for Statistics for Engineers | STAT 4706, Exams of Statistics

Download Solutions to Exam 1 for Statistics for Engineers | STAT 4706 and more Exams Statistics in PDF only on Docsity! WK > BOOM Answ we Icey Form A STAT 4706 - Statistics For Engineers Exam #1 Fall 2008 Name: Directions: You must do problem 1. Choose 3 out of the remaining 4 problems. If you do them all, only the first three will be graded. Show all work. Problem 1 Listed below are scenarios that need a specific confidence interval or hypothesis test. Select the letter from the possible choices that corresponds to the appropriate interval or test and mark it to the left of the number of the problem you're answering. Make sure to mark clearly on the exam paper. If the letter cannot be read by me, then the problem will be marked wrong. (3 pts. each...you get 1 point free!) A. One Sample z-test for G. One-Way Goodness of Fit Test. B. One Sample t-test for H. Two-Way Test of Independence or Homogeneity C. Two Independent Sample t-test | I. (1 — a) x 100% CI for w D. Paired t-test J. (1—a) x 100% CI for pu — pe E. Rank or Sign-Rank Test K. (1—a) x 100% CI for 6 F. Rank-Sum Test L. One or Two Sample Test for 7 or 7 — 72 We want to know if the average content of containers in a particular lubricant is 10 liters if we’re only given measurements from a random sample of 10 containers and the distribution of contents is normal. We have some data on the number of hours that two different types of scientific pocket calculators operate before a recharge is required. We want to determine if calculator A operates longer than calculator B on a full battery charge. Assume that the data does not come from a normal distribution. “wo oo . A marketing expert for a pasta-making company believes that 40% of pasta lovers prefer lasagna. If we counted the number of pasta lovers that prefer lasagna over other pastas from a random sample of 20 pasta lovers, we want to test if the expert’s claim is true. . We have some data on grades in a statistics course for a particular semester. We want to test if the distribution of grades is uniform. on . An independent consumer group tested radial tires from two major brands to determine whether there were any differences in the expected tread life. Assume that each test car only has one brand of tires. . Some data was recorded that represents the length of time to recovery for patients randomly treated with one & two medications to clear up severe bladder infections. We want to estimate the difference in mean recovery time for the two medications. = . The ocean swell produces spectacular eruptions of water through a hole in the cliff at Kiama, Australia, known as the Blowhole. Historically, the time between eruptions has been 60 seconds with a standard deviation of 10 seconds. The researcher wants to determine whether the true mean time between eruptions has increased from a random sample of the times at which 10 successive eruptions occurred. . In astudy conducted by the Department of Human Nutrition and Foods at VPI&SU, data was recorded on the comparison of sorbic acid residuals in parts per million in ham immediately after dipping in a sorbate solution and after 60 days of storage were recorded. We want to know if there’s sufficient evidence to say that the length of storage influences sorbic acid residual concentrations. oo Problem 2 The following data represent the running times (in minutes) of films produced by 2 motion-picture companies: Company 1 | Company 2 102 81 86 165 98 97 109 134 92 92 87 114 Test the hypothesis that the average running time of films produced by company 2 exceeds the average running time of films produced by company 1 by 10 minutes, against the alternative that the difference is not 10 minutes. a) (5 pts.) State the appropriate hypotheses for this test. You may purchase this answer for 5 points to make sure that the rest of the problem can be done correctly. Come and see me to purchase. Noi -Mr = he He ‘ay -A2 wat ) (20 pts.) First, construct and interpret a 90% confidence interval for 4; — jig, and then use that interval to test the hypotheses in part a). Assume that s; = a 88 = 89 = 30.2. 2 <= IO (30-2) es are (S/n. + 5*Mn2)? (Ce Ye+ sous * (EA)? (eo)? = ed aed in.) SZinde _sSae/n,): ie G = a S ey Qe at oe 2 = See Ae _ 10 ees = a (~¥2 yee (%-88)* _ ay = @44-uo) +t a as |e 1,64S (ie Oe ay 10, ORS Sie ane cencameepeete eects flrs produced hg Conperty C CxcedoYk avrag 7 tine Une Aoorce”) b [ 4 pees tice op fA doe, Foil delee Uo sh Pied ica ee anna to Yur - 35.5023 § py, 0M roy, *< | ><\ Problem 5 A food inspector examines 16 jars of a certain brand of jam to determine the percent of foreign impurities, A test for normality was done to see whether a nonparametric test was appropriate or not. Consider the following output from Minitab. Probability Plot of PctImpurities Normal wean 287 Site 08747 N 6 Ks 027 Pevalue 0.086 a) (5 pts.) Given the above graph and a 5% significance level, should we be using a nonparametric test? Plain vere Cok, so we rye Ho And cénarccy fa ea dota Aorran 4% Care bem a mevmal. dist. > oe a Nerporomelice fet b) (20 pts.) Now consider some Minitab output from a nonparametric test. Which parametric test could we have done instead of this? And test if the median percent of impurities in this brand of jam is not 2.5% with the same level of significance. Wilcoxon Signed Rank Test: PctImpurities GQ Ere.r sanphe £~ fet Test of median = 2.500 versus median not = 2.500 Unghted N for Wilcoxon Estimated Bah N Test Statistic B~ fedien HO f= 25° PctImpurities 16 16 35.5 0.098 2.100 Hen BF £ 2 Sv CH= OS. P-VehR = 095 >& > we fal do ayot Fs rena Conde phat te true jrradian prereset of Vrpuriles Co LS fy RS  Cn PAIRED COMPARISON EXPERIMENT (6 ONE OF THE MOST EFFECTIVE WAYS TO | REDUCE MATURAL VARIABILITY WHILE COMPARING TREATMENTS, FOR EXAMPLE, IN COMPARING HAND CREWAS, THE TWO BRANDS ARE RANDOMLY ASSIGNED TO GACH SUBJECT’S RIGHT OR LEFT WANDS THIS ELIMINATES VARIABILITY QUE TO SKIN DIFFERENCES. = (P40 2 ue wos Ox |