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INSTRUCTIONS: Special hints are given as to what classes you might refer to for each problem. You might want to read a problem, review the relevant classes, then work on the problem. GOOD LUCK!You don’t have to write on the test, you can just write on (and upload a scan or picture of) notebook paper with the problem number and section indicate (e.g, 1A…)Problem 1) : Below is a table of calls to a Poison center in Manhattan Kansas for exposures to disinfectants. (Review class 18 and 19) Calculate the Row and column totals, and do usual Chisquare analysis to see if there is an association between year and age for the poisonings at the .05 levelAge2018201920200–57668816–1918172420–59272840≥609385145Within each age group, 0-5, 6-59 (put two 6-19 and 20-59 together to get enough data), and 60 and up, run the Poisson difference tests we discussed to see if there are any interesting differences across the years. There will be 3 comparisons pre age group times 3 groups for 9 tests, Use FDR, not independent at the Q value of .1 to evaluate.What about the approach in B means some of the P values are not independent?Problem 2: You run an independent coffee shop that would provide bakery items along with coffee pre-pandemic. Once the pandemic starts you decide to see what sells. During a brainstorming session with your staff you quickly put together a list of things you can make or get to add to traffic in your storePrepared food: including Mini cakes that look like toilet paper rolls, Steak sandwiches, and Avocado sandwiches, Grocery Items: ? gallon milk cartons, bread, lettuce, Avocados, Toilet paper, dishwashing liquid, disinfectantHaving taken a statistics class you decide to run an experiment, stocking a little bit of every thing each day and see what sells . You get a website up and stock up, and allow one person in the store at a time to purchase and take away their packages. Apriori you assume Prepared has probability of 4/5 of being the most popular additionGrocery Items 1/5 of being the most popular additionYou assume the most popular will have a Poisson rate of 150 Sales per day while the less popular will have Poisson rate of sales of 45 sales per data. Going over the 1st day you quickly see (review class 19 and earlier classes on Bayes rule and Poisson)Prepared food: less than or equal to 60 sales, Grocery Items: greater than or equal to 160 salesCalculate the conditional probability of the observed sales per type of item given it is most popularCalculate the conditional probability of the observed sales per type of item given it is not most popularUsing Bayes rule calculate the conditional probability of each type of item being most popular given the observed sales. Problem 3: At the local pizza parlor people line up outside in their masks and proceed 1 at a time into the store to pay for and pick up the pizza. The manager who receives the orders for the pizzas wants to minimize peoples wait time. So she keeps track of the wait times for 25 people in mimutes: 40, 32, 5, 14, 7, 9, 12, 8, 9, 15, 12, 9, 15, 13, 14, 14, 7, 10, 13, 15, 18, 8, 18, 11, 7 (review classes 11,20)Check to see if the data is normal using the normal plot (you can upload the excel sheet along with your pictures of work by hand).If it looks normal, construct a 95% confidence bound for the mean wait time, otherwise construct a 95% confidence bound for the median wait timeProblem 4: You’re a brilliant inventor who recently won a noble prize, but you are obsessed with intelligence. You start a company and as part of hiring practices you institute an IQ test. You know the tests are designed to have an average of 100 and standard deviation upon retaking of the tests of 15. You want to be 99 percent sure that no one with an average IQ or lower is employed in each batch of 10 employees you test. (Review Classes 9,10,19) A) What is the critical IQ value that you use for this assuming you are using the Bonferroni method for achieving a level of .01 for every 10 tests. B) What is the power you have for detecting an IQ of 125 given the standard deviation of tests is 20 for the sub population with a mean of 125 (This was the measured IQ of the person who this describes at age 14). ................
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