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STOR 151 SECTION 1 FINAL EXAM DECEMBER 10 2019 This is an open book exam Course text personal notes and calculator are permitted You have 3 hours to complete the test Answers should be written in a blue book Personal computers and cellphones are not allowed If you have any queries about the meaning of a question ask the instructor for advice SHOW ALL WORKING even correct answers will not get full credit if it s not clear how Incorrect answers will gain substantial credit if the method of working is they were obtained substantially correct Answer six of the eight questions If you attempt more than six all the answers will be graded but only the best six complete questions will count Each question is worth a total of 20 points and the whole exam is worth 120 points which will be rescaled to a maximum of 40 for grading purposes Points for each individual part of a question are also given in square brackets Questions may be answered in any order 1 In an election being held in a certain foreign country there are three political parties Con servative Liberal and Socialist An opinion poll company is trying to determine how support for the three parties varies with age They sample 500 people who intend to vote from each of the three age groups 18 29 30 49 and 50 The participants in the survey state their support in the following table assume each participant supports one and only one party Age Group Conservative Liberal Socialist Total 18 29 112 188 200 500 30 49 232 130 138 500 50 Total 630 286 435 117 97 435 1500 500 a We are interested in testing whether the distribution of voters among the three parties varies with age group Show how to formulate this as a hypothesis testing problem and state H0 and HA Is it a test of equal column probabilities within each row or of equal row probabilities within each column or of independence 4 points b Carry out the test you proposed in a Compute the test statistic state the distribution the test is based on then state whether you accept or reject the null hypothesis Assume a signi cance level of 0 05 8 points c The pollster notices that support for the Liberal and Socialist parties seems very similar across the three age groups Without repeating the full calculations for the test of b but restricting to the Liberal and Socialist parties say whether you think there is an age dependent di erence in the support for those two parties 4 points d In non technical language state your conclusions about how support for the three po litical parties varies among the three age groups 4 points 1 2 In a game played at the NC State Fair players are invited to throw a baseball at a set of three blocks on a table if they knock all three blocks of the table they win a prize Past results suggest that the probability of winning a prize on a single play of the game is about 0 12 a Jenny plays the game six times What is the probability that she wins at least twice 6 points b Peter decides to keep playing until he wins once What are the mean and standard deviation of the number of throws he requires 7 points c Over the course of a two hour session the game is played 150 times What is the probability that at least 25 of those games result in winning a prize 7 points 3 According to data from the Census Bureau and the CDC adjusted for the purpose of this question some races are omitted 63 2 of Americans are non hispanic white 12 6 are non hispanic black 17 4 are hispanic 5 6 are Asian and 1 2 are native American Among non hispanic white adults over the age of 20 the proportion with type 2 diabetes is 12 3 For other races the corresponding proportions are non hispanic black 13 4 hispanic 13 9 Asian 13 9 native American 32 1 a Represent this information in the form of a tree diagram expanding the tree rst by race and then by prevalence of type 2 diabetes 6 points b What proportion of the total population is non hispanic white and has type 2 diabetes c What proportion of the total population is hispanic and does not have type 2 diabetes 4 points 4 points d For someone selected at random from the entire population if this person has type 2 diabetes what is the probability that he or she is native American 6 points 4 According to national statistics the mean number of hours of TV watched per day by 16 year olds in the US is 2 58 with a standard deviation of 1 71 The superintendent of the Chapel Hill Carrboro City Schools CHCCS is interested in knowing whether those gures apply in this district She randomly selects 61 16 year old students from the CHCCS system and asks them to record their viewing hours The mean for those students is 2 11 hours per day Assume that the standard deviation in the CHCCS school system is the same as the national value a Find a 99 con dence interval for the mean number of hours of TV watched per day by 16 year olds in the CHCCS system State any assumptions this involves 8 points b Test the null hypothesis that 2 58 Use a two sided test with signi cance level 0 05 8 points c Would you say that the results of a and b are in any way discrepant If so what is the main reason for this discrepancy 4 points 2 5 A study is conducted of the exercise habits of men and women in a university From each of ten dorms labelled A through J one man and one woman is randomly selected They are followed to determine how many minutes of exercise they take in minutes per day for a period of one week The results are as follows Dorm Man Woman Di erence A B 61 82 61 59 23 0 C 44 73 29 D E 96 76 35 60 16 61 F G H 57 70 57 58 12 0 70 46 24 I 59 40 19 J Mean 70 1 86 56 4 75 11 13 7 SD 15 5 12 9 22 8 a Analyze the data as a paired comparison experiment Is there a statistically signi cant di erence between the exercise times of men and women Use a two sided test with a signi cance level of 0 05 8 points b Analyze the data as a two sample experiment Is there a statistically signi cant di erence between the exercise times of men and women Use a two sided test with a signi cance level of 0 05 8 points c Which of the two tests do you feel is more appropriate in this case and state your overall conclusions 4 points 6 A woman claims to be able to tell …


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UNC-Chapel Hill STOR 151 - FINAL EXAM

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