252 1takehome081 2 22 08 ECO252 QBA2 FIRST EXAM February 2008 TAKE HOME SECTION Name Student Number and class time IV Do at least 3 problems at least 7 each or do sections adding to at least 20 points Anything extra you do helps and grades wrap around Show your work State H 0 and H 1 where appropriate You have not done a hypothesis test unless you have stated your hypotheses run the numbers and stated your conclusion Use a 95 confidence level unless another level is specified Answers without reasons usually are not acceptable Neatness and clarity of explanation are expected This must be turned in when you take the in class exam Note that answers without reasons and citation of appropriate statistical tests receive no credit Failing to be transparent about which section of which problem you are doing can lose you credit Many answers require a statistical test that is stating or implying a hypothesis and showing why it is true or false by citing a table value or a p value If you haven t done it lately take a fast look at ECO 252 Things That You Should Never Do on a Statistics Exam or Anywhere Else Problem 1 Doane and Seward A fast food restaurant has just started serving hot cocoa The management wishes to serve cocoa of an average temperature of 142 degrees 24 measurements of the temperature in 10 stores are taken You are manager of store a and will use the corresponding column where a is the second to last digit of your student number For example Seymour Butz student number is 543987 so he uses column x8 If that number is zero use column 10 You are testing to see if the mean for your store is 142 There will be a penalty if you do not make it clear what column you are using Row 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 x1 140 142 141 142 141 141 145 142 142 142 137 139 139 144 140 141 140 140 140 139 146 138 139 142 x2 142 143 141 142 139 142 144 145 143 143 141 139 143 144 140 138 141 140 142 140 138 139 142 141 x3 142 143 141 142 142 140 143 142 141 136 142 138 142 139 140 143 139 139 139 141 143 141 140 143 x4 143 138 140 140 142 139 142 139 145 139 142 138 142 141 142 141 141 140 142 141 143 141 140 140 x5 144 139 144 143 141 142 141 138 144 145 139 141 145 142 144 145 142 144 136 138 141 142 140 141 x6 142 142 142 140 141 141 137 142 139 141 141 143 141 142 140 142 142 142 139 142 143 143 142 140 x7 143 144 144 145 146 142 145 142 145 143 142 142 141 147 141 137 142 140 144 142 147 146 140 143 x8 146 145 144 144 145 144 141 141 144 144 139 142 141 142 144 145 139 142 143 146 142 144 144 146 x9 143 144 141 144 142 140 142 141 146 140 143 144 142 143 142 141 142 144 144 145 145 141 143 142 x10 143 139 145 144 145 142 141 140 142 142 142 146 142 143 142 140 144 143 141 144 143 141 139 142 Assume that the Normal distribution applies to the data and use a 98 confidence level a Find the sample mean and sample standard deviation of the incomes in your data showing your work 1 Your mean should be between 140 and 146 and your sample standard deviation should be around 2 b State your null and alternative hypotheses 1 c Test the hypothesis using a test ratio 1 d Test the hypothesis using a critical value for a sample mean 1 e Test the hypothesis using a confidence interval 1 1 252 1takehome081 2 22 08 f Find an approximate p value for the null hypothesis 1 g On the basis of your tests is the mean temperature correct in your restaurant Why 1 h How do your conclusions change if the random sample of 24 temperatures is taken on a day in which only 48 cups cocoa are sold 2 i Assume that the Normal distribution does not apply and test to see if the median is 142 Be careful What should you do with numbers that are exactly 142 2 12 j Extra Credit Do a 98 confidence interval for the median 2 Problem 2 Once again assume that the Normal distribution applies to the data in Problem 1 but that we know that the population standard deviation is 2 Our confidence level remains 98 but we are now testing the hypothesis that the mean is below 143 degrees a State your null and your alternative hypotheses 1 b Find the value of z that you need for a critical value for a 1 sided test if the confidence level is 98 You may use a confidence level of 99 if you wish for slightly less credit c Find a critical value for the sample mean to test if the mean is below 143 degrees 1 d Test the hypothesis that the mean is below 143 degrees using an appropriate confidence interval 2 e Using your critical value from 2b create a power curve for your test 6 f Assume that the population standard deviation is 2 How large a sample do you need to get a two sided 98 confidence interval with an error not exceeding 0 5 degrees 2 22 Problem 3 According to Doane and Seward about 13 of goods bought at a department store are returned An organization called Return Exchange will sell you a software product called Verify 1for which it makes the claims below Verify 1 is quickly operational And it authorizes returns even quicker Verify 1 identifies fraud and abuse at the point of return before they become liabilities to your brand equity or profits In stand alone mode this easy to use turnkey solution can be operational in 30 days and will reduce your return rate immediately without disrupting your business or IT configuration Verify 1 also integrates easily into your existing POS platform You set the policy Verify 1 enforces it With Verify 1 your returns are dealt with consistently utilizing advanced statistical modeling in combination with state return laws and your existing return policies At the point of return using the customer s driver s license or other valid identification Verify 1 automatically checks prior return behavior and authorizes or declines the transaction Customers identified as risks for presenting fraudulent returns are declined while legitimate returns are speedily accepted You take a sample of n items and find that there were x returns about 9 You are the manager of store a a is the last digit of your student number For example Seymour Butz student number is 543987 so he manages store 7 The sample size …
View Full Document
Unlocking...