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C291FE2012_FinalVersion_Apr9

B is gender v1 related to opinion about ubc support

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___b) Is gender (V1) related to opinion about UBC support services (V4)? ___c) Can second-year overall grade (V3) be explained by study hours (V6), amount spent on recreational activities (V9), and paid part-time work (V5)? ___ & ___ d) Are there equal percentages of males and females (V1) who do paid part-time work (V5)? (Two answers are possible here – both are needed ) ___e) Do males and females (V1) achieve different first-year overall grades (V2)? ___f) Is the rate of Facebook users (V8) different from the Canadian percentage? ___g) Does monthly expenditure on recreational activities (V9) exceed $250? ___h) Are first-year overall grades (V2) and second-year overall grades (V3) different on average? ___ i) Is second-year overall grade (V3) related to study hours (V6)? ___ j) Is mode of travel (V7) related to study hours (V6)? 8
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Question 5 (Total 12 marks) “Ford had a Model T; you have a t model!” a) Automobile insurance appraisers examine cars that have been involved in accidental collisions to assess the cost of repairs. An experiment was done to examine whether different appraisers produce significantly different assessments of minor collisions. The experiment was designed so that a total of 10 cars were used and each car was assessed by each appraiser. Here are the data. Car 1 2 3 4 5 6 7 8 9 10 Appraiser 1 1650 360 660 1050 890 750 470 1270 550 730 Appraiser 2 1440 380 600 920 930 650 410 1080 480 770 A researcher did some Excel analysis to compare the mean appraisals of the two appraisers, but he was not sure which procedure to use – the matched pairs t-test or the two-sample t-test, so he tried both. Here are the outputs from his two analyses. The test names and output labels are as they appear in Excel. OUTPUT 1 OUTPUT 2 t-Test: Two- Sample Assuming Unequal Variances t-Test: Paired Two Sample for Means Appraiser 1 Appraiser 2 Appraiser 1 Appraiser 2 Mean 838 762 Mean 838 762 Variance 154618 105507 Variance 154618 105507 Observations 10 10 Observations 10 10 Hypoth. Mean Diff. 0 Hypoth. Mean Diff. 0 df 17 df 9 t Stat 0.471 t Stat 2.496 P(T<=t) one-tail 0.322 P(T<=t) one-tail 0.017 t Critical one-tail 1.740 t Critical one-tail 1.833 P(T<=t) two-tail 0.643 P(T<=t) two-tail 0.034 t Critical two-tail 2.110 t Critical two-tail 2.262 Is there enough evidence at the 5% significance level that the appraisers differ in their assessments? (Note: You do not have to do any computations here ; just choose the most appropriate result from the two tests reported above and interpret it! Don’t forget to state your hypotheses, P-value and a conclusion.) (i) State the appropriate null and alternative hypotheses for this comparison. H 0 : _________________ H a : _________________ (ii) Which output is the more appropriate? (Circle one) OUTPUT 1 OUTPUT 2 (iii) Give a short explanation for your choice. 9
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(iv) Write out the formula of the test statistic you decided to use. (v) State the appropriate P-value. ___________ (vi) Write a conclusion, in one sentence only. (vii) What is meant by a Type I Error in this situation? In each pair of choices in italics and parentheses, circle the correct answer. The test concludes ( there is / there is not ) a difference between the appraisers with respect to mean appraisals when, in fact, ( there is / there is not ) truly a difference.
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