ADM 2304 -- ASSIGNMENT 1 Due Date: Friday, October 9, 2015 at midnight Instructions: 1. Your assignment should be uploaded to Blackboard Learn and in pdf format. 2. You may use Minitab or other software for any calculations. However, you must do manual calculations when asked. You may paste your output onto your assignment; however, this output does not replace any of the steps outlined below. 3. If you are performing a hypothesis test, make sure you state the hypotheses, the level of significance, the decision rule in terms of the critical value, the test statistic or p-value, your decision (whether to reject or not to reject the null hypothesis), and your conclusion in managerial terms. 4. The data from both Minitab data files can also be found in the Excel file Assign1Data.xls. 5. Remember to include your integrity statement. 1. [ 10 marks ] On 19 October 2015, Canadians will vote in a federal election. During the last federal election in 2011, 39.62% voted Conservative, 30.63% voted NDP, 18.91% voted Liberal, 9.98% voted Bloc Quebecois, and 6.78% voted Green. a b c A recent poll of 1000 respondents found the three major parties in a virtual tie, with the Greens lagging behind at 4.4%. Test whether there is evidence at the 5% level of significance to show that the support for the Greens has dropped. Show your manual calculations. What sample size would be required to obtain a 99% 2-sided confidence interval for the true proportion of Green Party support with a margin of error of 1%? Suppose that, in a random sample of 17 University of Ottawa students, only 4 indicated a preference for the Conservatives. Test whether this is sufficient evidence to indicate that the level of support for the Conservatives among U of O students is lower than the 39.62% share of the popular vote in 2011. Use the .01 level of significance and explain how you would calculate the p-value for this test. Why does this not allow us to infer anything about the national level of support for the Conservatives? 2. [ 9 marks ] A file in the assignments area on Blackboard Learn called incomes.mtw contains data on the median and average incomes for neighbourhoods in Ottawa-Gatineau. a. b. Treating the average incomes as the population, use Minitab to calculate the population mean. Set aside all population information until part d. Now use Minitab (Calc Menu - Random Data - Sample from Columns) to draw twenty samples of size n = 30. This procedure must be replicated twenty times (note that if you open up the same sampling dialog box each time from the menu, then you only have to replace the last destination column with the next one). Using each sample, use Minitab to calculate a 90% confidence interval estimate for the population mean, assuming you do not know the population standard deviation (this interval estimation can be done in one operation on all twenty columns). 1 c. d. e. 3. For the first sample, confirm the Minitab generated interval by calculating the interval manually. Display the sample data graphically and comment on whether the relevant assumption regarding the population distribution is warranted (state clearly the assumption needed to justify the interval estimation). Count the number of intervals that contain the true value of the population mean from part a. What proportion of students would you expect to count 18 of their 20 intervals that contain the population mean? [ 6 marks ] The file BMIsamples.mtw contains two samples of BMI values from the male and female populations. Test at the 0.05 level of significance whether there is sufficient evidence here to show that the average male BMI (in the population) exceeds 25. Explain whether your test satisfies the underlying assumptions, with reference to graphical evidence, and show your manual calculations. 4. [ 10 marks ] Two of the columns, OWmale and OWfemale, in the same dataset code the BMI values as: 0 - if BMI 25.4 (these are considered \"not overweight\"); 1 - if BMI 25.5 (these are considered \"overweight\"). a. b. c. d. Test whether there is sufficient evidence to show that the proportion of overweight males (proportion of males who are overweight) is different than the proportion of overweight females in the population. Use the critical value approach and the 0.05 level of significance. Perform the test manually after using Minitab to summarize the data (note that the mean coded value in each sample is the sample proportion). Now find the p-value for your sample result and explain how you would find the p-value if you did not have statistical software to perform the test for you. Finally calculate manually the 95% 2-sided confidence interval for the true difference between the proportions of overweight males and overweight females. Explain how the results in parts b and c are consistent with your conclusion in part a. 2 ID medinc avginc 5050001 22003 30712 5050001 32561 43037 5050001 34458 45465 5050001 35852 45244 5050001 34211 46165 5050001 35950 59782 5050002 45997 56223 5050002 46110 56659 5050002 62659 76240 5050002 28553 35768 5050002 48925 56247 5050003 33755 44450 5050004 28907 36017 5050005 34566 45859 5050006 57487 73829 5050007 40621 53843 5050007 18962 22511 5050007 39889 59975 5050008 35508 44221 5050009 40538 46970 5050010 22922 29957 5050011 32545 39461 5050011 32293 46131 5050011 29638 43241 5050012 20092 27422 5050013 31046 39871 5050014 18761 27003 5050015 30889 46990 5050016 56880 76310 5050017 50690 69418 5050018 49759 71849 5050019 54427 71722 5050020 25589 37411 5050020 37627 51426 5050021 29279 33879 5050022 20198 28259 5050023 32685 41844 5050023 44998 50549 5050024 33066 45073 5050025 45446 56563 5050026 35133 41003 5050027 31573 36386 5050028 32294 40762 5050029 27206 33495 5050030 28984 37989 5050031 38494 45527 5050032 35820 44912 5050032 48766 66393 5050033 49223 58695 5050033 38420 55536 5050034 66985 91446 5050035 36906 46435 5050036 60912 84839 5050037 40802 46866 5050038 31419 40122 5050039 32933 40235 5050040 38304 46418 5050041 23024 36987 5050042 18407 27372 5050043 36409 45672 5050044 62954 84782 5050045 48421 60685 5050046 28670 39804 5050047 59236 80433 5050048 53750 61152 5050049 46206 54407 5050050 26904 40948 5050051 25272 38627 5050052 41020 51189 5050053 27953 43264 5050054 36880 59591 5050055 45212 52555 5050056 29131 37026 5050057 55953 66771 5050058 55787 79653 5050059 46387 55287 5050060 31625 40669 5050061 27477 34081 5050062 34706 44743 5050062 23979 33265 BMIfemaleBMImale OWfemale OWmale 24.3 24.4 0 0 24.4 28.4 0 1 28.8 21.4 1 0 24.1 28.8 0 1 27.1 30.1 1 1 36.3 24.2 1 0 30.5 21.3 1 0 23.8 23.7 0 0 20.6 22.4 0 0 30.9 24.9 1 0 23.5 24.5 0 0 19.6 25.5 0 1 22.4 35.2 0 1 22.5 30.5 0 1 24.5 26.1 0 1 19.8 31.1 0 1 22.3 23.4 0 0 28.9 25.4 1 0 20.6 24.9 0 0 18.9 26.2 0 1 23.2 23 0 0 20.3 24.9 0 0 20.1 23.3 0 0 26.3 25.1 1 0 21.3 26.2 0 1 21.9 28.5 0 1 21.6 24.2 0 0 17.8 28.2 0 1 24.9 29.6 0 1 22.8 27.1 0 1 34.3 26.4 1 1 24.2 25.6 0 1 20.7 26.1 0 1 33.7 23.7 1 0 24.2 21.6 0 0 32.8 24.8 1 0 22.5 27.8 0 1 21.3 22.8 0 0 21.2 28.4 0 1 35.2 1 21.8 0 23.9 0 23.6 0 24.1 0 26.2 1 29.5 1 29.8 1 26.1 1 22.8 0 5050100 5050101 5050102 5050103 5050104 5050110 5050120 5050120 5050120 5050121 5050121 5050122 5050122 5050122 5050123 5050123 5050124 5050124 5050124 5050124 5050125 5050125 5050125 5050125 5050125 5050125 5050125 5050125 5050126 5050126 5050126 5050126 5050127 5050130 5050130 5050131 5050131 5050132 5050133 5050134 5050135 5050135 5050135 5050136 5050136 5050137 5050137 5050137 5050137 5050138 5050139 5050140 5050140 5050140 5050140 5050140 5050141 5050141 5050141 5050141 5050141 5050141 5050141 5050141 5050141 5050141 5050151 5050151 5050151 5050151 5050151 5050151 5050151 5050160 5050160 5050160 5050160 5050160 5050160 5050160 5050160 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