stat217 wint05 exam2

stat217 wint05 exam2 - Print Name: Stat 217, Winter 2005...

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Unformatted text preview: Print Name: Stat 217, Winter 2005 Exam 2 (Ver. A) Instructor: Dr. Jimmy Doi This is a closed book, closed notes examination. The use of a calculator is permitted. Including this page, the exam has a total of 5 pages. There are a total of 11 questions. There are 100 points possible on this exam. Provide all answers on this exam and Show all work where appropriate. If necessary, you may use the back of these pages if you need more space. If you have any questions at all during the exam, please do not hesitate to come up and ask. Best wishes and good luck! Read and sign the following before you submit the exam: By signing below, I understand that giving or receiving help on this exam is a violation of academic regulations and is punishable by a grade of in the course and possible further action by Cal Poly Judicial Affairs. Acts of violation include revealing (actively or passively) any information about the exam to any member of Prof. Doi’s Stat 217 class who is currently taking or not yet taken the exam. By signing below, I pledge not to violate academic regulations. Signature: Question 0: MAKE SURE YOUR NAME APPEARS ON THE FRONT OF THIS EXAM. Question 1: [4 points total] Suppose it is known a randOm variable Y follows the Normal dis- tribution with mean it and standard deviation 0. Given a sample of any integer size n 2 l (i.e. n = 1, 2, 3, the sampling distribution of X is necessarily Normal. (Circle One: FALSE) Question 2: [4 points total] In statistical inference, our goal is to infer informatio statistic through the value of a parameter. (Circle One: TRUE FAL E gem-(an. Question 3: [4 points total] When using a density curve as a probability model for a variable X, if we consider two constants a and b, the probability P(o < X < b) is equal to the distance from a to b on the X axis. (Circle One: TRUE Question 4: [4 points total] The distribution of values taken by a statistic, for a given sample size, from the same population is known as the sampling distribution a I tistic. (Circle One: @ FALSE) Question 5: [4 points total] Suppose we conduct a hypothesis test for H0 : ,u : no and we discover the corresponding p—value = 0.8211. What can we conclude based upon this p—value? There is weak evidence against H0. Mixers is moderate to strong evidence against H0. M There is moderate to strong evidence to support Ha. ’(fi’) We cannot remark on the strength of evidence without specifying the form of the alternative hypothesis, H“. )e‘f We cannot remark on the strength of evidence without specifying the value of or, the significance level. Questidn 6: [18 points total] The automatic opening device of a military cargo parachute has been designed to open when the parachute is 200 meters (m) above the ground. Suppose open— ing altitude actually has a normal distribution with mean 200 m and standard deviation 30 m. Equipment damage will occur if the parachute opens at an altitude below 100 m. —u-—u—I-'- Bombs Away.’, the company that produces the cargo parachute, has introduced a new deployment mechanism. Having fallen in love with statistics in Stat 217 under the guidance of your favorite instructor, you decided to switch your major, get a degree in statistics, and you are now happily employed as a lead statistician for Bombs Away!. The opening altitude of the new chutes is normally distributed with unknown mean ,u. The popu— lation standard deviation 30 m. Your team drops In of these new cargo chutes and measures the altitude at which they open and find the sample mean is 241.6 mi (a) [8 points] Find a 99% confidence interval for the mean altitude for the pepulation of parachutes produced using the new deployment mechanism. CW7» “- Z. .S‘lko zul.Ui2..%‘"\\o $6: : ZLHMZE Ztikl’be [an we. \ amuse] (b) [4 points] What is the margin of error in this setting? 24. HEB (c) [6 points] Assuming we still desire a 99% confidence level, suppose you want to reduce the margin of error you found in part (b) by half. Compute the sample size necessary to do this. 1 z. I (ironed/303] =£ “'75 : Lia/52.2 2. Qflflm 4: do l2.‘2.?_. \‘2 252. Question 7: [24 points total] The time needed for college students to complete a certain paper and pencil maze follows a normal distribution with a mean of _§O_ seconds and a standard deviation of 3 seconds. Researchers wonder whether the mean time would decrease for students that complete the maze while listening to classical music. (30’ 2,") Suppose the time needed for college students to complete the maze while listening to classical music is normally distributed with mean u and standard deviation 3 seconds. A group of 25 college students attempt the maze while listening to classical music. Their average completion time turns out to be 3:28.11 seconds. (a) [16 pts] Based upon the experts' suspicions, conduct the appropriate hypothesis test at the 5% level. Be sure to specify the necessary hypotheses and the basis for your conclusion. Do not simply say “REJECT H9” or “DO NOT REJECT H0” briefly explain why you came to your conclusion. Show all work where appropriate. to art- 53 Ha 71.4270 2: 2554—30 2 a —2.,Ld7l- gfxrss *0 ’P(2<~2.Loe§Tovo\e PF 00% i—t——-—\—\\ Qcémrt its @%°b becwae 0 [l '0’: .0098 is) low Wm 05 (b) [8 Pts] Sketch the sampling distribution of E assuming H0 is true and shade the area in the distribution that corresponds to the p-value for the hypothesis testing problem above. Virus) M32. LA Question 8: [22 points total] Below we have a table of all Epossible arrangements of boys and girls among a total of 4 children. For example, BBGG means the first two children are boys and the last two are girls. Suppose all 16 arrangements are equally likely. BBBB GBBB-J BGGB GGBG BBBG" BBGG GBGB GBGG BBGB I BGBG GGBB BGGG BGBBJ GBBG GGGB GGGG Let Y be the number of boys among the four children. (a) [5 pts] List the possible values of Y. angel (b) [3 pts] What is the probability of any one of the arrangements given in the table above? l/IL; (c) [4 pts] What is the probability that there are three (and only three) boys among the four children? Lille -— 1/L{ (d) [10 points] Find the probability distribution of Y. Question 9: [6 points total] Reading an article on the levels of toxins discovered in local water source, researchers measured the toxin level for each of 25 samples they inspected and reported the sample mean, E. In their report, they stated “the standard error of the mean was found to be 0.52”. __——-- Based on this information, What was the sample standard deviation 3 for these measurements? Em;.'~'o'2. ; 5 BC CQZ>61353 ED \lfh: Srikp Question 10: [10 points total] The level of nitrogen oxides (NOX) in the exhaust of a particular car model varies with mean_0._9 grams per mile (g/ mi) and standard deviation 0.15 g/ mi. A company has 125 cars of this model in its fleet. Assume 125 is large enough to apply the Central Limit m 3 - Cl ieorem‘IWhat is the NOX level (K) such that the probability the sample mean will be less than m “B m ?C\£L .6) y ‘25 . r , / Fwd J?) to. abut fl Helpful Formulas are? (2 n: [Town as. ‘7 elm“ ( ) + — do 1::th {Knot 6ft“: .2:— SQW am. Qfl Tit‘fi «Hy-e mic—mm rfl <2" ‘9 beamincia ‘ 0 Check Blackboard (under Course Project) for the project handout, data set file, and the list of groups and members. If you have not contacted your group members and exchanged email/phone information already, be sure to do so (this is your responsibility). If you have trouble contacting your group members, please let me know immediately. I The new HVV assignment has been posted on Blackboard — please get started on it as soon as possible. 0 Have a GREAT weekend! Helpful Formulas for Exam 2 (Stat 217) Suppose X1, X2, . . . ,Xn is a random sample Where each X,- follows the same distribution with mean a and standard deviation 0. Suppose 7 is the mean of this random sample. Then, 7 has meanzp, and has standard deviationch/ a: 2 n = (z a) 4— m fizz“: Women. Tif— cmfidenca~ fl ' fl homo o’me Solutions: Exam 2 [Version A/B], Winter 2005 Stat 217 The solution set is applicable for BOTH versions A and B. Somehow, I accidently left Version B identical to Version A this will not occur on the final. (1) — (5) See marks on exam for correct answer. (6) (a) 241.6 :I: 2.576% : 241.6 :1: 24.44 - (b) The margin of error is 24.44 (see above) 3 2 (c)'n = 2m" = %‘22 z 6.322 = 39.99 —» 40 (7) (a) H0 : a = 30 versus H, : ,u < 30. _ 23.4 — 30 = 42.67 3N2? Z p-value = P(Z < —2.67) = 0.0038. Reject H0 at the 5% level since 0.0038 3 0.05. (b) Sketch the N (30, 0.6) distribution (0.6 = 3/ m). Mark the location of 28.4 appropriately (using adequate spacing) and shade everything from 28.4 and to the left. (8) (a) The possible values of Y are 0, 1, 2, 3, 4 (b) 1/16 (c) 4/16 Y Probability 0 1/16 : 0.0625 1 4/16 : 0.25 (d) 2 6/16 2 0.375 3 4/16 = 0.25 4 1/16 = 0.0625 = 0.52 aim sin Thus, 5 = 0.52 - (J5) = 2.6. (10) This is a backwards normal calculation for the sampling distribution of E. The location on the N(0, 1) distribution with about 15% of the area to its left is -1.04. ——o.9 055/7125 < "1'04 E H 0.15/\/125- (41.04) + 0.9 5 0.8860 ...
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This homework help was uploaded on 02/13/2008 for the course STAT 217 taught by Professor Staff during the Winter '01 term at Cal Poly.

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stat217 wint05 exam2 - Print Name: Stat 217, Winter 2005...

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