252y0821 10/20/08ECO252 QBA2 SECOND EXAMMarch 28, 2008TAKE 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 a31 and the number of business majors who have loans to a24 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. Ag Ch Engg Lib Bus Sci Tech Loan 32 37 98 89 24 31 57 None 35 50 137 124 51 29 71 a) Compute the proportion of non-science majors that have loans in order to test the hypothesis that sciencemajors are more likely to have loans than other majors. Tell which group you consider sample 1. State0H and 1H 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 youwill find the corresponding values of E and EEO2, 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.1252y0821 10/20/08(ii) To do a test of the alternative hypothesis 211: ppH , where 111nxp and 222nxp , use the command below, substituting your numbers for 1x, 1n, 2x and 2n.MTB > PTwo 1x 1n 2x 2n;SUBC> Confidence 99.0;SUBC> Alternative 1;SUBC> Pooled.The computer will print back 1x, 1n,111nxp , 2x, 2n and 222nxp a p-value for a z-test and 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 1x. A sample of ‘ego strength’ of the ‘Fit’ faculty is labeled 2x. 21xxd .Use a 95% confidence level in this problem.The professor has computed 1xSum ofFat scores = 64.96, 21xSum of squares of Fat scores= 307.607, 2xSum of scores of Fit = 90.02, 22xSum of squares of Fitscores = 581.239, dSum of diff = -25.06 and2dSum of squares of diff = 51.8198. Row Fat Fit Diff 1x 2x 21xxd 1 4.99 6.68 -1.69 2 4.24 6.42 -2.18 3 4.74 7.32 -2.58 4 4.93 6.38 -1.45 5 4.16 6.16 -2.00 6 5.53 5.93 -0.40 7 4.12 7.08 -2.96 8 5.10 6.37 -1.27 9 4.47 6.53 -2.06 10 5.30 6.68 -1.38 11 3.12 5.71 -2.59 12 3.77 6.20 -2.43 13 5.09 6.04 -0.95 14 5.40 6.52 -1.12To 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 1321nn 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 yourselfconsiderable 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 n Mean SE Mean StDev Median Fat 14 4.640 0.184 0.690 4.835 Fit 14 6.430 0.115 0.431 6.400 diff 14 -1.790 0.196 0.732 -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 1x and 2x 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 1x and 2x 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)2252y0821 10/20/08c) Assume that 1x and 2x are independent random samples. How
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