Statistics exam


THIS IS THE REAL QUESTIONS:  (a) Writing your answers in a Word document or PDF document. If you choose to go that route, please ensure you are submitting your exam in one of these formats. This is, by far, the easiest way for me to grade.  1. Conventional wisdom holds that among Canadians who donate to charities, the average total donation per year is $400. You want to test whether this conventional wisdom does in fact represent the true parameter value by running a two-tailed hypothesis test. You randomly sample 80 Canadian donors and find a mean of 430, with a standard deviation of 100. (8 points) a) Detail the steps of the hypothesis test you would run at a 95% confidence level, including the conclusion and its interpretation. b) Demonstrate how the answer arrived at in (a) is validated by running a 95% confidence interval.  2. A provincial government runs a limited series of TV advertisements to press citizens to respect COVID–19 restrictions. Because its budget is limited, it cannot afford to air the ads everywhere across the province, meaning that those living in certain media markets are exposed to the ads, while those living in other areas are not. The government starts to doubt that the ads are having an effect even in those areas where they are broadcasted. You are hired to measure whether the ads are, in fact, having an impact. You randomly sample two groups of people: 202 voters who have been exposed to ads, and 245 voters who have not. In the first group, 79 indicate that they intend to respect the restrictions. In the second group, 89 claim they will abide by them. Assuming that the ads alone are responsible for a possible, statistically meaningful difference between the two groups, are the ads having an impact? (8 points) i. Answer by running a two-tailed hypothesis test with 90% confidence. Outline every step, the conclusion and its interpretation. ii. Demonstrate and explain how the answer arrived at in (a) is validated by running a 90% confidence interval. 3  3. You hear on the evening newscast a pundit claim that Canadians who live in Ontario tend to show greater attachment to the British monarchy than do those live either in Quebec or in Atlantic Canada. Since you have now grown to develop a deep skepticism toward what you hear from journalists and the media, you decide to test this proposition by collecting a random sample of citizens across the country. You ask them to tell you their level of attachment to the monarchy – either very attached, somewhat attached, not very attached, or not at all attached. You lump the first two and the last two to arrive at two basic categories (attached vs. not attached), and produce the following contingency table. (8 points) Very/somewhat attached Not very/not at all attached Total Ontario 32 (30.9) 26 (27.0) 58 Quebec 35 (34.2) 29 (30.0) 64 Atlantic Canada 28 (30.0) 28 (26.1) 56 Total 95 83 178 a) Conduct a Chi-Squared hypothesis test with 80% confidence to evaluate whether or not Ontarians are more likely than others to profess attachment to the monarchy. Make sure to detail every step, provide a conclusion, and interpret that conclusion. b) What is the value 30.9 telling us in this table? Interpret in the context of the problem. 4  4. Suspecting that civil disobedience is linked with certain social, political, and economic factors, you try to explain the number of acts of civil disobedience in a city in a 12-month timeframe on the basis of four variables: the percentage of residents aged 18-30 per 1000 residents (x1); the percentage of residents who are male (x2); the gap between the wealthiest and poorest residents, in thousands of dollars (x3); and whether the city has a policy specifically pertaining to countering civil disobedience, with “no” coded as 0 and “yes” coded as 1 (x4). After collecting and entering your sample data into statistical software, you run a multiple regression model with a 95% confidence level. The software spits out the following results. (9 points) n = 314 R2 = 0.78 Disobedience acts Coefficient (Standard Error) z P > z 95% Confidence Interval Percent 18-30 1.13 (0.08) 2.18 0.015 [1.01, 1.15] Percent male 0.04 (0.02) 2.04 0.021 [0.01, 0.07] Income gap 0.24 (0.11) 1.79 0.038 [0.11, 0.37] City policy -0.05 (0.09) 1.12 0.131 [-0.17, 0. 07] y-Intercept -0.61 (0.10) 1.29 0.099 [-0.70, -0.52] a) Write out the full prediction equation for this regression model. b) If you were putting a star next to the variable(s) who meet statistical significance at the P < 0.05 level, which variable(s) would get one? c) What is the value -0.61 telling us in this table? Interpret in the context of the problem. 5 d) Would increasing our confidence level to 99% change our conclusion (i.e. significance test conclusion) about β3? If so, why? If not, why not? e) Interpret the R2 value in the context of this problem. f) How many control variables does this model have?  5. On the October 9, 2014 edition of CBC’s The National, host Peter Mansbridge convened a panel to discuss the state of public opinion polling amidst what many are considering failures (most notably in predicting electoral results). In wrapping up the segment, Mansbridge asked the three panelists what advice they would have for ordinary Canadians who would want to evaluate whether a poll result they are hearing about can be trusted. One of the three panelists replied that people should “look around them” – i.e. to their circle of friends, relatives, and colleagues – to see whether the result or trend that a poll is reporting is reflected in the people around them. Is this sound advice to offer to ordinary Canadians wishing to evaluate whether a poll’s results are credible? Why or why not? (2 points) Bonus. You have now immersed yourself in the basic concepts of what arguably constitute the pinnacle of quantitative research method in the social sciences. Yet a colleague of yours, skeptical of quantitative methods, tells you that for all you have learned, it is no match for what qualitative methods provide. Is he correct? If so, why? If not, why not? Make sure to refer to chi-square and regression in your answer. (1 point)Practice Exam 2

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