252y061t 10 31 06 Open in Print Layout format ECO252 QBA2 SECOND EXAM November 7 8 TAKE HOME SECTION Name Student Number Class days and hour III 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 Note Look at 252thngs 252thngs on the syllabus supplement part of the website before you start and before you take exams 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 from now on neatness means paper neatly trimmed on the left side if it has been torn multiple pages stapled and paper written on only one side 1 Row 1 2 3 4 5 6 7 8 9 10 11 12 13 14 A bank is testing various ways to serve walk in customers It tries 10 different new ways to organize this service and gets the following results Each result can be considered as a random sample of 14 times that it takes a teller to serve ten walk in customers The data is presented below Method 1 is the method currently in use You are asked to compare method 1 with one other method by comparing the mean or median time it takes to serve the customers and to find out if there is a significant difference between the methods On the basis of your results you can conclude that i the old method is better ii the new method is better or iii more information is needed to make a decision The second method to compare to method 1 is determined by the second to last digit of your student number if it is 0 use method 10 if it is 1 use method 11 If it is 2 3 4 etc use the method with the corresponding number Label this problem clearly with the number of the method that you are comparing with Method 1 Method 1 2 9 3 9 2 6 3 1 3 9 2 6 3 3 3 0 3 5 3 1 3 2 2 4 4 0 4 3 2 2 8 2 6 2 6 2 9 2 9 2 8 2 3 2 4 2 0 2 5 2 4 2 0 4 1 4 3 3 2 6 2 7 3 2 2 8 3 6 2 1 2 3 2 6 2 6 2 9 2 4 2 3 0 5 4 7 4 7 7 2 9 4 3 2 7 3 4 4 4 5 5 3 4 3 4 3 5 4 0 3 4 4 1 3 8 5 2 4 13 4 5 8 1 5 9 8 2 7 2 7 4 5 2 3 5 8 4 8 4 2 5 8 6 1 6 6 6 3 7 9 7 1 9 10 1 4 5 2 9 9 9 3 0 31 5 3 5 5 3 9 8 5 3 7 3 5 8 4 4 3 3 3 11 9 3 7 3 0 2 9 3 6 5 4 4 4 3 0 4 3 5 4 Minitab gives us the following computations for Method 1 8 3 4 8 3 4 2 3 2 11 0 3 6 2 9 2 8 3 5 5 3 4 3 2 9 4 2 5 3 9 3 5 3 4 3 8 3 4 3 6 3 5 4 8 3 5 5 3 3 7 3 4 3 6 3 8 3 8 10 2 3 6 9 3 3 5 3 3 0 3 3 6 1 3 1 2 6 4 4 15 0 6 9 2 1 10 4 n 14 x 3 271 11 3 4 4 4 3 1 3 6 4 4 3 1 3 8 3 5 4 0 3 6 3 7 2 9 4 5 4 8 s x 0 155 s 0 580 Minimum 2 400 Q1 2 825 x 50 3 150 Q3 3 900 Maximum 4 300 For other information see the end of this document You can assume that the data for method 1 has an underlying Normal distribution Use a 95 confidence level a Compute a standard deviation for the method that you are comparing with Method 1 Carry at least as many significant figures as you see in the Minitab computations above 1 b Test for a significant difference between the methods on the assumption that your method represents data taken from the Normal distribution and the times have approximately equal variances Use a test ratio critical value or a confidence interval 3 or all three 6 c Assume that the data represents a Normally distributed population but the variances are not equal 4 extra credit 252y061t 10 31 06 Open in Print Layout format d Assume that the Normal distribution does not apply 4 e Test to see if the data from your method is Normally distributed 3 f Test to see if the standard deviations of the two methods are equal 1 g On the basis of the sections of this problem that you have been able to do write a recommendation 1 11 16 2 A researcher asked a group of artists and non artists whether they believed in extra sensory perception The data assembled is as below Of 114 artists 58 77 believed in extrasensory perception 35 96 more or less believed in extrasensory perception and the remainder did not believe Of 344 non artists 37 50 believed in extrasensory perception 53 20 more or less believed and the remainder did not believe a Is there any association between being an artist and believing in ESP 6 b Do a confidence interval for the difference in proportions who do not believe in ESP among artists and non artists Is the difference significant 2 24 3 A researcher wants to see if the type of vehicle driven affects safety related behavior The researcher observes the following behavior at a stop sign on a rural intersection Behavior Sedan Wagon Van SUV Stopped 180 24 30 14 Rolled through 107 18 10 20 Ran sign 60 8 11 16 Personalize the data as follows To the number 180 add the last digit of your student number a Is there an association between the vehicle driven and behavior 5 b Cut down the number of rows in the problem by adding together the people who stopped and rolled through Assume that you were testing the hypothesis that the proportion of individuals who who ran the stop sign was independent of the type of vehicle driven and that you had rejected your null hypothesis Use a Marascuilo procedure to find the 6 possible differences between proportions and to find out if there are any pairs …
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