252y0561s 11 14 05 ECO252 QBA2 SECOND EXAM Nov 8 9 2005 TAKE HOME SECTION Name Key Note that complete solutions for 1 and 2 were only worked out for two versions of these problems III Neatness Counts Show your work Always state your hypotheses and conclusions clearly 19 points 1 A state is trying to figure out whether the background on highway signs makes a difference In order to do this two samples of 15 individuals are shown a number of slides rapidly The slides have either a green or a red background You are trying to find out whether there is a difference between the number of slides correctly read between those with a red or a green background To do so you will compare the mean or median as appropriate to the distribution To personalize the data look at the third digit from the end to decide what red data you will use Call the column that you pick rj and compute a column called dj with the formula dj green rj Example Seymour Butz s student number is 976512 so he picks column 5 and used d5 green r5 Tell me what column you are using If you compare means state your hypotheses both in terms of 1 and 2 and in terms of D 1 2 Row 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 green 8 10 6 5 9 7 3 7 7 3 6 6 8 3 10 r0 9 10 9 4 9 9 8 7 5 6 10 8 8 9 9 r1 5 9 5 7 6 7 9 8 7 5 7 5 8 7 7 r2 7 10 11 9 8 8 8 7 9 9 7 7 10 7 6 r3 6 12 7 10 12 10 9 11 9 8 7 6 11 13 8 r4 5 6 5 6 5 11 8 8 7 9 10 7 7 6 5 r5 8 9 6 10 7 7 5 6 11 9 10 7 7 8 8 r6 9 7 6 7 8 7 6 6 7 7 5 7 10 7 6 r7 7 9 10 11 11 6 11 6 9 7 7 7 9 8 8 r8 10 9 7 10 6 6 7 8 8 7 9 11 6 8 7 r9 5 6 6 7 10 10 10 13 9 6 8 6 7 8 10 Minitab computed some basic statistics from the data which will help you in some parts of this problem Variable green r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 N 15 15 15 15 15 15 15 15 15 15 15 Mean 6 533 8 000 6 800 8 200 9 267 7 000 7 867 7 000 8 400 7 933 8 067 SE Mean 0 601 0 458 0 355 0 368 0 581 0 488 0 435 0 324 0 456 0 408 0 573 StDev 2 326 1 773 1 373 1 424 2 251 1 890 1 685 1 254 1 765 1 580 2 219 Minimum 3 000 4 000 5 000 6 000 6 000 5 000 5 000 5 000 6 000 6 000 5 000 Q1 5 000 7 000 5 000 7 000 7 000 5 000 7 000 6 000 7 000 7 000 6 000 Median 7 000 9 000 7 000 8 000 9 000 7 000 8 000 7 000 8 000 8 000 8 000 Q3 Maximum 8 000 10 000 9 000 10 000 8 000 9 000 9 000 11 000 11 000 13 000 8 000 11 000 9 000 11 000 7 000 10 000 10 000 11 000 9 000 11 000 10 000 13 000 a Display the numbers that you are using in columns and compute a sample mean and sample standard deviation for the d column 1 In this problem assume that the red and green data are two independent samples Use a confidence level of 95 b Assume that you believe that the normal distribution does not apply to the data and compare the means or medians as appropriate 4 c You suspect that the data has the Normal distribution Test to see if the Normal distribution applies Use a test that I taught you 3 1 252y0561s 11 14 05 d You decide that the Normal distribution applies to the data but do not know if the variances are equal Test them for equality 1 e You conclude that the underlying distributions are Normal and that the population variances are equal Compare the means or medians as appropriate Use a test ratio critical value or a confidence interval 4 or all three 6 15 f Extra credit You conclude that the underlying distributions are Normal and that the population variances are not equal Compare the means or medians as appropriate Use a test ratio critical value or a confidence interval 5 or all three 7 2 In fact the data on the previous page applies to a single sample of 15 individuals That is the first line of your worksheet tells you how the first person in the sample did when showed the same slides with red or green backgrounds This applies to a and b in this question Use a confidence level of 95 a Assume that you believe that the normal distribution does not apply to the data and compare the means or medians as appropriate 3 b You assume that the data has the Normal distribution Compare the means or medians as appropriate 3 c For any part of one of these problems tell me which one compute a confidence interval that you would use to compare means if your alternate hypothesis was H 1 2 1 2 23 d For the same part as you used in c find a p value for the null hypothesis 2 25 These results are all supposed to look to me as you did them by hand But what I don t know won t hurt me If you want to check your results by computer you might try to use the following Minitab routine If you put green in C1 and label columns with headings like rj dj and dsqj Seymour called his green r5 d5 and dsq5 The routine below with appropriate changes to rj dj and dsqj will compute much of the stuff above though not in the right order Note that to do a Wilcoxon signed rank test by hand you will have to drop all zeroes from the d column Computations for comparing c1 and rj MTB MTB MTB MTB MTB MTB MTB SUBC MTB MTB MTB SUBC MTB SUBC MTB SUBC let dj c1 rj let dsqj rj rj print c1 rj dj dsqj describe c1 rj dj sum dj ssq dj TwoSample c1 rj Pooled TwoSample c1 rj Paired c1 rj VarTest c1 rj Unstacked WTest 0 0 dj Alternative 0 Mann Whitney 95 0 c1 rj Alternative 0 If you want to fake the calculations for the Mann Whitney test try this Procedure …
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