252x0521 4 01 05 Page layout view ECO252 QBA2 SECOND HOUR EXAM April 4 2005 Name Hour of Class Registered Circle 9am 10am Show your work Make Diagrams Exam is normed on 50 points Answers without reasons are not usually acceptable I 8 points Do all the following Make diagrams x N 21 6 If you are not using the supplement table make sure that I know it 1 P 0 x 21 00 2 P x 10 22 3 P 7 00 x 30 4 4 x 035 252x0521 4 01 05 Page layout view II 24 points Do all the following 2points each unless noted otherwise Note the following 1 This test is normed on 50 points but there are more points possible including the take home You are unlikely to finish the exam and might want to skip some questions 2 A table identifying methods for comparing 2 samples is at the end of the exam 3 If you answer None of the above in any question you should provide an alternative answer and explain why You may receive credit for this even if you are wrong 1 Computer Problem Bassett et al 400 children were divided into two groups The first and larger group were taught Mathematics by traditional methods The second group was taught by an experimental method Test scores were recorded and are available The computer analysis of the data is shown in the three tests below The First Test was done using method 2 The researcher was reprimanded by her supervisor for assuming that the population variances were equal so she ran the Second Test without assuming equal variances Because she was very annoyed at her supervisor she ran the third test for equal variances The output is below Assume a significance level of 1 Do not do any unnecessary computations First Test MTB TwoSample c1 c2 SUBC Pooled SUBC Alternative 1 Two Sample T Test and CI x1 x2 Two sample T for x1 vs x2 N Mean StDev SE Mean x1 250 68 45 7 96 0 50 x2 150 70 62 7 06 0 58 Difference mu x1 mu x2 Estimate for difference 2 17521 95 upper bound for difference 0 87525 T Test of difference 0 vs T Value 2 76 P Value 0 003 DF 398 P Value 0 002 DF 343 Second Test MTB TwoSample c1 c2 SUBC Alternative 1 Two Sample T Test and CI x1 x2 Two sample T for x1 vs x2 x1 x2 N 250 150 Mean 68 45 70 62 StDev 7 96 7 06 SE Mean 0 50 0 58 Difference mu x1 mu x2 Estimate for difference 2 17521 95 upper bound for difference 0 91322 T Test of difference 0 vs T Value 2 84 Third Test MTB VarTest c1 c2 SUBC Unstacked Test for Equal Variances x1 x2 F Test normal distribution Test statistic 1 27 p value 0 107 a Turn in your first computer assignment 2 b Look only at the first test i What are the null and alternative hypotheses 1 ii Can we conclude that the experimental method is better What are the numbers in the output that bring you to this conclusion 2 c Make a drawing of an almost Normal curve Label the center of the curve with a zero and show the area under the curve that is the p value 1 2 252x0521 4 01 05 Page layout view d Look at the results of the second test Do they look different to you from the results of the first test Why 2 e Look at the results of the third test What do you think were the null and alternative hypotheses Was her supervisor right that she should not have assumed equal variances Why 2 8 Questions 2 5 refer to Exhibit 1 Exhibit 1 Schiffler Adams A new feed is supposedly superior to what you have used in the past to feed your pigs You divide your pigs into two troops of 60 pigs each After one month the results are as follows You want to decide if the new feed is actually better Assume that the sample data comes from two Normal populations with equal population variance Old Feed x1 175 9 s1 12 n1 60 New Feed x 2 180 2 s 2 19 n 2 60 2 What is the alternative hypothesis a 1 2 b c 1 2 1 2 1 2 d e None of the above 3 What is a b c d e sd 0 5 0 7 1 5 2 9 8 4 4 If we do not reject the Null hypothesis do we decide that there is a reason to switch to the new feed 1 5 Change your assumptions to assume that both samples have a population standard deviation of 15 Find a 93 two sided confidence interval for the difference between the means 3 Is there a significant difference between the means Why 1 17 3 252x0521 4 01 05 Page layout view Questions 6 and 7 refer to Exhibit 2 Exhibit 2 Lees The net income figures for seven regions in which Smelly Welly Dirt Devourer is sold are given before and after a reorganization Region Before After Difference Reorganization Reorganization 1 40 62 22 2 35 49 14 3 42 39 3 4 30 28 2 5 55 55 0 6 63 66 3 7 36 40 4 The researcher decides that the Wilcoxon Signed Rank test for paired samples is appropriate The region with a tie is dropped from consideration leaving 6 pairs for this test only The test is one sided Minitab gives the following sample statistics for the data for use in Problem 7 Use 05 Description Variable Before x1 After Difference x2 d n 7 Mean 43 00 7 7 48 43 5 43 SE Mean StDev 4 46 11 80 5 15 3 49 13 62 9 24 6 In the Wilcoxon Signed Rank Test the number that you compare to the values in the Wilcoxon Signed Rank Test Table is 3 a 3 b 3 5 c 17 d 17 5 e 18 f 18 5 g None of the above write in the correct number and show your work 20 7 If we change our assumptions to state that the underlying distribution is Normal we should not be using the Wilcoxon Signed Rank Test If we use a test based on the mean we have all of the following a Confidence Interval D d t 2 s d b Test Ratio t d D0 sd c Critical Value d cv D0 t 2 s d On the basis of the information above find d s d and the numbers of degrees of freedom If you do any calculations make sure that I know what they are 4 24 4 252x0521 4 01 05 Page layout view 8 A marble machine is recalibrated and the owner is afraid that it is producing marbles that are too small The standard size is 12mm The following results pop out after 105 diameters are fed to the computer One Sample T x1 …
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