Instructions: 1. You may use Minitab or other software for any calculations. However, you must show your manual calculations when asked. You may paste your output to show your use of Minitab; however, this output does not replace any of the steps outlined below. This means that answers that are exclusively Minitab output may receive only one mark. 2. If you are performing a hypothesis test, make sure you state the hypotheses, the level of significance, the rejection region, the test statistic (and p-value, if requested), your decision (whether to reject or not to reject the null hypothesis), and a conclusion in managerial terms that answers the question posed. These steps must be completed in addition to any Minitab output. 3. The data in the Minitab data files can be found in the file Assign1Data.xls. 1. In the 2015 federal election, 39.47% of the electorate voted for the Liberal party, 31.89% for the Conservative party, 19.71% for the NDP, 4.66% for the Bloc Quebecois, and 3.45% for the Green party. (a) A recent poll of 1500 respondents found that 29.3% support the Conservative party. Test whether this is sufficient evidence to conclude that the level of support has dropped since the election. Use the 5% level of significance and show your manual calculations. (b) Suppose you want to estimate the national level of support for the Conservatives using a 95% 2-sided confidence interval with a margin of error of 1%. What sample size would be required? (c) Suppose that, in a random sample of 23 University students, only 3 indicated a preference for the Conservatives. Test whether this is sufficient evidence to indicate that the level of support for the Conservatives among the students is lower than the 31.89% share of the popular vote in 2015. Use the .05 level of significance and show how you would calculate the p-value for this test. 2. The file bmi.mtw contain the Body Mass Index (BMI) for a sample of men and a sample of women. Two of the columns, OW_male and OW_female 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) 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 (if you use descriptive statistics, the mean coded value in each sample is the sample proportion). (b) Explain how to find the p-value manually (indicate what probability has to be calculated). (c) Finally calculate manually the 95% 2-sided confidence interval for the true difference between the proportions of overweight males and overweight females. (d) Explain how the results in parts (b) and (c) are consistent with your conclusion in part (a). 3. (a) Test at the 0.05 level of significance whether the sample of male BMI observations is enough to show that the mean BMI for males exceeds 25.5. Show your manual calculations (you may use Minitab to summarize the sample data). (b) Explain whether your test satisfies the underlying assumptions, with reference to a boxplot of the sample data. 4. [10 marks] The file OttawaMedianIncomes.mtw contains data on the median incomes (medinc) of census dissemination areas in Ottawa. (a) Treating this set of data as the population, use Minitab to calculate the population mean for the medinc variable. Set aside all population information until part (e). (b) Examine a boxplot and histogram of the population data. Explain if the means of all possible random samples of size 40 from this population would form a normal distribution. Answer (c) and (d), without the information from (a) and (b). (c) Now use Minitab (Calc Menu - Random Data - Sample from Columns) to draw twenty samples of size n = 40 from the Ottawa medinc population. 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). For each sample, use Minitab to calculate a 95% 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, but not in Minitab Express). (d) For your first sample, confirm the Minitab generated interval by calculating the interval manually. Display the sample data using a boxplot and comment on whether the relevant assumption regarding the population distribution is warranted given your sample (state clearly the assumption needed to justify the interval estimation). (e) Count the number of intervals out of your twenty that contain the true value of the population mean from part (a). MedInc 32908 35306 34956 44511 42716 34530 31157 35051 46143 55872 61669 41318 32042 38921 34252 38444 36718 42227 37513 42193 46632 33481 36038 38484 47727 35954 38620 39036 38932 42326 34479 24825 41163 48945 38938 41559 49619 44211 43912 42144 63131 25563 32064 35290 42133 29746 30313 30940 37392 bmi_male bmi_femalOW_male OW-female 26.9 19.4 1 0 29.9 23.1 1 0 28.2 24.8 1 0 30.5 18.4 1 0 25.6 29.9 1 1 31.3 24.5 1 0 27.6 19.8 1 0 23.3 19 0 0 25.1 22.9 0 0 29.6 17.7 1 0 22.1 25.6 0 1 24.2 25.6 0 1 26.3 22.1 1 0 31.3 23.9 1 0 22.1 27.7 0 1 23.8 22.1 0 0 26.2 28 1 1 30.3 32.3 1 1 23.4 29.1 0 1 19.7 35.2 0 1 28 22.1 1 0 27.2 19.1 1 0 27 25.2 1 0 21.7 18.9 0 0 24.9 24.3 0 0 30.5 21.9 1 0 25.6 28.1 1 1 29.3 16.3 1 0 33 18.4 1 0 27.1 23.8 1 0 30.2 22 1 0 29 1 24.9 0 22 0 25.6 1 41803 38896 38427 32712 39751 34690 38963 36622 39273 44084 45255 44186 47294 32233 38418 31377 32252 33995 30403 29959 24888 41526 34658 35058 36562 29993 42414 39642 41184 56165 42068 47164 41270 31583 63086 46788 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