1. 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 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.
b 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%?
c 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. 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. Treating the average incomes as the population, use Minitab to calculate the population mean. Set aside all population information until part d.
b. 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).
c. 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).
d. Count the number of intervals that contain the true value of the population mean from part a.
e. What proportion of students would you expect to count 18 of their 20 intervals that contain the population mean?
3. 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. 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. 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).
b. 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.
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.