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WCU ECO 252 - ECO 252 Second Exam

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252y061t 10/31/06 (Open in ‘Print Layout’ format) ECO252 QBA2 SECOND EXAMNovember 7-8TAKE 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 0H and 1H 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. 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 is2, 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 Row 1 2 3 4 5 6 7 8 9 10 11 1 2.9 2.8 2.6 7.7 2.4 6.6 3.5 3.4 3.5 2.3 3.4 2 3.9 2.6 2.7 2.9 13.4 3.7 8.4 8.3 3.4 6.9 4.4 3 2.6 2.6 3.2 4.3 5.8 9.7 4.3 4.2 3.8 3.3 3.1 4 3.1 2.9 2.8 2.7 1.5 1.9 3.3 3.2 3.4 5.3 3.6 5 3.9 2.9 3.6 3.4 9.8 10.1 11.9 11.0 3.6 3.0 4.4 6 2.6 2.8 2.1 4.4 2.7 4.5 3.7 3.6 3.5 3.3 3.1 7 3.3 2.3 2.3 5.5 2.7 2.9 3.0 2.9 4.8 6.1 3.8 8 3.0 2.4 2.6 3.4 4.5 9.9 2.9 2.8 3.5 3.1 3.5 9 3.5 2.0 2.6 3.4 2.3 3.0 3.6 3.5 5.3 2.6 4.0 10 3.1 2.5 2.9 3.5 5.8 31.5 5.4 5.3 3.7 4.4 3.6 11 3.2 2.4 2.4 4.0 4.8 3.5 4.4 4.3 3.4 15.0 3.7 12 2.4 2.0 2.3 3.4 4.2 5.3 3.0 2.9 3.6 6.9 2.9 13 4.0 4.1 0.5 4.1 5.8 9.8 4.3 4.2 3.8 2.1 4.5 14 4.3 4.3 4.7 3.8 6.1 5.3 5.4 5.3 3.8 10.4 4.8Minitab gives us the following computations for Method 1. n14, x3.271, xs0.155,s0.580, Minimum2.400 1Q2.825, 50.x3.150, 3Q3.900, Maximum4.300. 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 atest 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) [11]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) [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 SUVStopped 180 24 30 14Rolled through 107 18 10 20Ran sign 60 8 11 16Personalize 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 whowho ran the stop sign was independent of the type of vehicle driven and that you had rejected yournull hypothesis. Use a Marascuilo procedure to find the 6 possible differences between proportions and to find out if there are any pairs of vehicle types where the difference between the proportions is insignificant. (4) [33]There will be extra credit offered for verifying your results using Minitab. A chi squared test can be done by putting columns of data in without any totals and following the procedure used in the first part of 252chisqx2. To compare two columns you can use the following


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