252y0821 10 20 08 ECO252 QBA2 SECOND EXAM March 28 2008 TAKE HOME SECTION Name Student Number Class hours registered and attended if different IV Neatness Counts Show your work Always state your hypotheses and conclusions clearly 19 points In each section state clearly what number you are using to personalize data There is a penalty for failing to include your student number on this page not clarifying version number in each section and not including class hour somewhere Please write on only one side of the paper Be prepared to turn in your Minitab output for the first computer problem and to answer the questions on the problem sheet about it or a similar problem 1 Moore McCabe et al A large public university took a survey of 865 students to find out if there was a relationship between the chosen major and whether the students had student loans The students majors were categorized as Agriculture Child Development Engineering Liberal Arts Business Science and Technology Before you start personalize the data as follows Let a be the second to last digit of your student number Change the number of Science majors with loans to 31 a and the number of business majors who have loans to 24 a for every part of this problem The total number of students in the survey will not change Put your version of the table below on top of the first page of your solution Use a 99 confidence level in this problem Loan None Ag 32 35 Ch 37 50 Engg 98 137 Lib 89 124 Bus 24 51 Sci 31 29 Tech 57 71 a Compute the proportion of non science majors that have loans in order to test the hypothesis that science majors are more likely to have loans than other majors Tell which group you consider sample 1 State H 0 and H 1 in terms of the proportions involved and also in terms of the difference between the proportions explaining whether this difference is a statistic from sample 1 minus a statistic from sample 2 or the reverse 1 b Use a test ratio to test your hypotheses from a 2 c Use a critical value for the difference between proportions to test your hypotheses from a 2 d Use an appropriate confidence interval to test your hypotheses from a 2 e Treat each major separately and test the hypothesis that the proportion of students that have loans is independent of major 4 f If you did section 1e follow your analysis with a Marascuilo procedure to compare the proportion of business students that have loans with the proportions for the other 6 majors Tell which differences are significant 3 14 g Extra credit Check your results using Minitab i To do a chi squared test on an O table that is in Columns c22 c28 simply put the row labels in Column c21 and print out your data Then type in ChiSquare c22 c28 The computer will print back the columns with their names but below each number from the O table you will find the corresponding values of E and O E 2 E the contribution of the value of O to the chi square total Use the p value to find out if we reject the hypothesis of equal proportions at the 1 significance level 1 252y0821 10 20 08 ii To do a test of the alternative hypothesis H 1 p1 p 2 where p1 x1 x2 and p 2 use n1 n2 the command below substituting your numbers for x1 n1 x 2 and n 2 MTB PTwo x1 n1 x 2 n 2 SUBC Confidence 99 0 SUBC Alternative 1 SUBC Pooled The computer will print back x1 n1 p1 x1 x2 x 2 n 2 and p 2 a p value for a z test and n1 n2 Fisher s exact test results should be somewhat similar to the z test and a 1 sided 99 confidence interval 2 Moore McCabe et al An absolutely tactless psychology professor has divided faculty members into categories the professor labels Fat and Fit A random sample of scores on a test of ego strength of the Fat faculty is labeled x1 A sample of ego strength of the Fit faculty is labeled x 2 d x1 x 2 Use a 95 confidence level in this problem Row Fat Fit Diff The professor has computed x1 Sum of x1 Fat scores 64 96 x12 Sum of squares of Fat scores 307 607 x 2 90 02 Sum of scores of Fit x 2 2 Sum of squares of Fit scores 581 239 d Sum of diff 25 06 and d 2 Sum of squares of diff 51 8198 1 2 3 4 5 6 7 8 9 10 11 12 13 14 4 99 4 24 4 74 4 93 4 16 5 53 4 12 5 10 4 47 5 30 3 12 3 77 5 09 5 40 x2 6 68 6 42 7 32 6 38 6 16 5 93 7 08 6 37 6 53 6 68 5 71 6 20 6 04 6 52 d x1 x 2 1 69 2 18 2 58 1 45 2 00 0 40 2 96 1 27 2 06 1 38 2 59 2 43 0 95 1 12 To personalize the data remove row b where b is the last digit of your student number Please state clearly what row you removed At this point you will have n1 n 2 13 rows of data You will need the mean and variance of all three columns of data if you do all sections of this problem You can save yourself considerable effort by using the computational formula for the variance with the sums and sums of squares that the professor computed with the value or value squared of the numbers you removed subtracted The professor got the following results Variable Fat Fit diff n 14 14 14 Mean 4 640 6 430 1 790 SE Mean 0 184 0 115 0 196 StDev 0 690 0 431 0 732 Median 4 835 6 400 1 845 Your results should be relatively similar Credit for computing the sample statistics needed is included in the relevant parts of this problem State hypotheses and conclusions clearly in each segment of the problem a Assume that x1 and x 2 are independent random samples and test the hypothesis that the population mean of the ego strength of the fit faculty is above the population mean of the fat faculty Assume that the data comes from the Normal distribution and that the variances for the fit and fat populations are similar 3 b Extra credit Assume that x1 and x 2 are independent random samples and test the hypothesis that the population mean of the ego strength of the fit faculty is above the population mean of the fat faculty Assume that the data comes from the Normal distribution and that the variances for the fit and fat populations are not similar 3 2 252y0821 10 20 08 c Assume that x1 and x 2 are independent …
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