Statistics 201 Practice Exam 3 for Spring 2014 From Fall 2013 This practice exam is provided solely for the purpose of familiarizing you with the format and style of the Stat 201 exams There is no explicit or implicit guarantee that the upcoming exam will ask similar questions If you use the practice exam as your only tool to help you prepare for the upcoming exam you most likely will not do well on the exam You should still do the things you would have done if you did not have access to this practice exam such as re read the text go over your class notes re work the online homework problems and look at the list of exam topics provided and make sure that you understand all the concepts listed within it The topic of Decision Trees was on last semester s final exam but was moved to Exam 2 this semester Therefore this practice exam is slightly shorter that what you should expect 1 Note All problems requiring calculations should be reported to THREE decimal places unless stated otherwise 1 Question 1 was a Decision Tree question This topic will not be on Exam 3 2 First USA a major credit card company is planning a promotional offer for their current cardholders The offer will give double airline miles on purchases for the next 6 months if the cardholder goes online and registers for the offer To test the effectiveness of the campaign First USA recently sent out the offer to a random sample of 50 000 cardholders From this random sample 1184 customers registered for the promotional offer i 2 points Two conditions for a confidence interval for a single proportion are the Randomization and 10 conditions which are both met in this instance Name the final condition corresponding to the confidence interval for a single proportion and verify whether or not it is met ii 3 points Regardless of your answer in part i assume all three conditions for a sample proportion are met The central limit theorem says that the sampling distribution for a sample proportion approximates a certain distribution with a specific mean and a specific standard deviation when all three conditions are met Choose the correct sampling distribution model that is relevant for this scenario regarding First USA s offer for their current cardholders iii a N b tn 1 p c N p d N p 4 points Using a critical value Z of 2 054 calculate a 96 confidence interval for the true population proportion of those cardholders who will register for the offer Interpret this confidence interval in the context of the problem 2 Question 2 continued iv 2 points If the registration rate for this offer is less than 2 then First USA would deem the expense of the campaign to be too costly Based on the confidence interval you calculated in part iii is this evidence to suggest that the new campaign isn t worth the expense Briefly explain If you have no answer for part iii use 0261 p 0295 for your interval which is NOT the correct answer v 2 points Suppose First USA used simulation to replicate this new campaign 1000 times with 1000 random samples of 50 000 cardholders Therefore one thousand 96 confidence intervals were produced Approximately how many 96 confidence intervals out of those 1000 would you expect to contain the true population proportion of cardholders who had register for this offer Circle the best answer a b c d 996 96 960 9 6 3 3 A pharmaceutical company is seeking approval for a new drug that lowers blood pressure in people who have medically documented hypertension high blood pressure This drug is better than current drugs on the market because it works so quickly Patients must take other drugs for hypertension for at least three weeks before any helpful reduction in blood pressure can be noted The new drug works within two days of the initial dose which is extremely beneficial for patients who are at risk of stroke because of extremely high blood pressure levels Because the drug alters blood pressure so quickly a few patients in the preliminary medical trials have experienced extreme dizziness which could increase the risk of falling The pharmaceutical company contends that this side effect is minimal thus leading to the null hypothesis that the drug is safe to market The Federal Drug Administration FDA therefore has the burden of collecting data to either support or refute the claim of the pharmaceutical company i 3 points In the context of this problem state the null and alternative hypotheses ii 3 points In the context of this problem what is a Type I error iii 3 points In one complete sentence identify a consequence of making the Type I error you defined in part ii iv 2 points In general how does a researcher reduce the probability of a Type II error 4 4 A survey by Harris Interactive for job site CareerBuilder com explored the possible relationship between type of job and whether or not workers admitted to falling asleep on the job 700 individuals that were either IT professionals or government professionals were randomly selected and asked in an anonymous survey to provide this information The following data were collected i 3 points If you were to do a Chi Square test of independence on these data what are the null and alternative hypotheses ii 4 points The table above is missing an Expected Cell Count and missing a Cell Chi Square value Calculate these values below 5 Question 4 continued iii 6 points There are three conditions that must be met for the Chi Square test of independence to be valid What are they and are they met in this case Condition 1 is Is condition 1 met Circle one YES NO Briefly justify your choice below Condition 2 is Is condition 2 met Circle one YES NO Briefly justify your choice below Condition 3 is Is condition 3 met Circle one YES NO Briefly justify your choice below 6 Question 4 continued iv 2 points Regardless of your answers to part iii use the output below to test your hypotheses using 0 0025 Circle one a Reject the null hypothesis b Fail to reject the null hypothesis Briefly explain why you decided to circle the answer that you circled above v 2 points Simply saying reject or fail to reject the null hypothesis is not a complete conclusion State your conclusion in the context of this problem below 7 Question 4 continued vi 4 points The table on the left below is the default output from JMP for this analysis This table contains the percentages that make up the Mosaic Plot Use this table to fill in the four blanks in the bars of the Mosaic Plot that represent the height of each bar 8 5 A new
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