Solutions to Exam I, Math 442, Spr06 - “mafia(WNW woe...

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Unformatted text preview: “mafia (WNW woe exam; 1. (30 pts.) In an article published in the Journal of the American Medical Association‘, two similar groups of adults over 55 years of age were followed for a roughly seven year period. The members of one group received a daily (400 IU) dose of vitamin E while the members of the other group received a daily placebo. The summary statistics: __-_ —- Number of Sub ects “— Is there evidence that vitamin E helps prevent cancer deaths? To answer this question, let pa = Proportion of Cancer Deaths in the population taking placebo (Control Group) p, = Proportion of Cancer Deaths in the population taking placebo (Treatment Group) and use a = 0.05. a. State the two rel b. Sketch a standard normal curve, label the accept H0 and the reject H 0 regions along the axis. Indicate the numerical value(s) separating the regions. (Chaim/é MOM P flnfiflr— 0C = .05 (/v \_./Wr——/ 9 (VJ—Ho (‘45 lit/66+ ”D c. Compute the relevant Z statistic ‘ A ’_ A __ 2::- - ’73/5'94 Z ' a Fr) (0) +2)@ =156/5§2. ’ p*((r V903; , ;:I7J+/56 d. Come to a decision 584+5£Z @ (A!) flEfiL E .1176:ch 421K , ___..____________ mm»: a [45905 ) ‘ ' The HOPE and HOPE-T00 Trial InVestigators (2005), “Effects of Long-term Vitamin E Supplementation on Cardiovascular Events and Cancer”, JAMA, vol. 293, pp. 1338 -— 1347 (http: //jama.ama- assn.orycgi/content/short/293ll U] 338). 2. (30 pts.) Headability i I e ability of a cylindrical piece of m-'tev= to be shaped int the head of a bolt, ' ew or other cold formed part 5 ~ -_ : king. An article described the :.- e': - headability impact test applied ecimens of aluminum killed steel -Wecimens of silicon killed steel. Summary statistics (with a standard “rating num . - used for units) appear in the table below: Material Sample Mean Sample Standard ‘ Deviation Aluminum Killed Steel 59 1.19 I m; = 3%. Silicon Killed Steel 5' 1.08 I n, ; 30 Is there evidence that the mean headability for aluminum (#4) is higher than that for silicon (as)? Conduct the relevant test by completing the items below (suppose that the two sample sizes are sufficiently large). Use a significance level of a = 0.05. a. State the two relevant b. Sketch a standard normal curve, label the accept Ho and reject H0 regions along the axis. Indicate the numerical value(s) separating the regions. ”p.190“? pm ,1 25—— Prw =— = b , 05 W W e. Compute the relevant Z statistic W Ha I- 545 WA] Cf}? " is) (a) 2 . 7.4-? 5 d. Come to am ‘ @CcpmflfilL/nlo Ell/KAZi WW/‘A-7M5) 2 “New methods for assessing cold heading quality", Wire Journal International, October 1996, pp. 66-72. 3. (20 pts.) In 1938 Pratt and Woodruff3 conducted an extrasensory perception (ESP) study in which individuals were repeatedly asked to determine which of 5 symbols — square, wavy line, circle, star, cross — appeared on a card seen only by a study investigator. If the subjects were guessing then they would have 1 chance in 5 of guessing correctly on any one trial. The subjects in this study correctly guessed 12,489 of the symbols in 60,000 trials. If the subjects were only guessing, estimate the chance of getting 12 489 or more correct out of 60,000 using the Central Limit Theorem. Do not worry about the “continuity correction” here. Do give me a numeric estimate. * C : fi- (QM/46W 80.20le m: 6‘0/0002 f z [/5 WPMxIWy vamh w m (17009 ”5%) ’2 hp :G0/000)(//;> 3m 6. (54’0”)C “3)(4/5) :: ¢7,?[ / P(/Z/¢?75 C f 6o/050) 2:". \ If éalppo— limo») __ T #1,???» r220“) ‘27.?5’ 77-” 2 gram?) — £01.79) g [—I [email protected] 3 See, for example, Hansel, C.E.M. (1966), ESP: A Scientific Evaluation, Scribner’s, New York, NY, pp. 86-89. 4. (20 pts. ) Below, is a plot of diamond price (in Singapore dollars) against diamond weight (in carats) for 308 round diamonds: 15000 10000 pfice 5000 02 03 04 as as 07 as 09 to L1 carats Here are some summary statistics on these two variables: Variable Mean Standard Deviation / carats 0.6309 0.2772 price $5,019 $3,403 Correlation of carats and price = 0,945 3. Give the least squares line of price in terms of the number of carats. 43 V’Wi 45,019+ 7f: 31133—(mwr: .6709) ' ”L771, ‘ Chu, Singfat (2001), “Pricing the C’s of Diamond Stones”, Journal of Statistics Education, vol. 9, no. 2, http: //www. amstat. org/publications/jse/v9n2/datasets. chu. html. b. Predict the price, in Singapore dollars, for a 0.60 carat diamond. c. The largest diamond in the dataset weight 1.09 carats and sells for a price of $9,107. Find the associated residual. ‘ A flux 2 470/34,; 05/ wao (.0? ”am (MATS IN 0.) flea/Wm, = £6»wa ’— 'r’né-Ovcrsw : 59,?15- 4‘ la/afips’ ¢»$//133.°8 { d. There are, altogether, 308 residuals. What is the typical size of these residuals? ..A u 5 -; I A Z. “-1. 3? 07: gt) ’1‘" ("- V‘“ SID ...
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