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UW-Madison ECON 310 - homework08

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Econ 310 Professor Wallace Fall 2013 Homework #8 (Due in lecture on Tuesday November 12) Note: Questions 2 through 4 are test type questions that would be worth 40-60 points apiece (depending) on a 120 point exam. The last part(s) of the questions involve power calculations which are typically worth between 10 (2.F.) and 20 points (3.H-3.I, 4.E.-4.F.). If your goal is a perfect score on the next exam you need to be able to work through each these problems (all of 2, 3, and 4) in about 30 minutes. If your goal is a B on the next exam then you need to be able to complete the parts that don’t involve power calculations with a near perfect score in about 30 minutes. 1. Picture Drawing. Given the following assumptions: 221212,XNnn   Draw pictures for each hypothesis tests below. Label your distributions (and where they center), horizontal axes, critical value, rejection region, significance level, the type I error region, type II error region, and the statistical power. A. 00:,H   significance level at , the true ,a   and the hypothesis test has a power of 0.50. B. 00:,H   probability of committing Type I error is , and true ,a  and the probability of Type II error is 0.75. C. Given the same test in part b), draw graphs(s) with 'a   where you will have statistical power equal to 0.75. D. On the same graph as in part c), draw the distributions where the sample size are doubled but the test and true (alternative) value of  remains the same. E. 00:H   where true ,a   and a the statistical power is 0.75.2 2. Virginia’s Governor’s Race. In recent years Virginia has served as a political bellwether for the United States. In 2008 and 2012 Virginian voted for Obama with a vote margin similar to the vote margin for the country as a whole and elected Democrat Senators Mark Warner and Tim Kaine. In the off presidential year election of 2009, however, Virginians voted to elect conservative Republicans Bob McDonnell and Ken Cuccinelli to the positions of governor and attorney general. Because of Virginia’s status as a bellwether the Virginia governor’s race of 2013, which pits acting Attorney General Ken Cuccinelli against longtime Clinton loyalist Terry McAuliffe, has been closely watched by the national media. Many pundits believe that the Government shutdown of October of 2013 has damaged the Republican brand and Ken Cuccinelli’s and has improved Terry McAuliffe’s chances at winning the governorship. A Washington Post poll of 562 likely voters conducted from September 19 to September 22 (before the shutdown) found support for McAuliffe at 47 percent. A more recent Washington Post Poll of 762 likely voters conducted from October 24th to October 27th (after the shutdown) found that support for McAuliffe at 51 percent. In this question you will examine whether there is strong evidence to indicate support for McAuliffe has grown in the time between when the two polls where taken . A. What is the (population) parameter of interest? B. Construct a 95% confidence interval for the differences in the proportion of likely voters who would vote for McAuliffe in late-October versus mid-September? Use the confidence interval in a sentence. C. What is the most appropriate hypothesis to test to determine whether there is strong statistical evidence that support for McAuliffe has grown between mid-September and late-October? Be sure to state the null and alternative hypothesis. D. What is the distribution of the appropriate sample statistic for conducting the hypothesis test in part C. under the null? E. Conduct the hypothesis test in part C. At which standard significance levels can you reject the null? F. Suppose the support for McAuliffe grew from 45 percent to 50 percent of likely voters between mid-September and late-October. What is the approximate power of the hypothesis test conducted in part C assuming a significance level of 0.01. Be sure to clearly state any assumptions that you make.1 1 You should need to make an assumption about the value of p.3 3. Mosquito Nets and Malaria Prevention. Malaria is a huge problem in Sub-Saharan Africa, where an estimated 800 thousands people die annually from the disease. Malaria is mosquito born disease and thus efforts at controlling the disease have focused eradicating the mosquitoes that carry the disease, limiting the exposure of people to mosquitoes, and trying to ensure that people that develop malaria are properly diagnosed and treated. Recent attention has focused on the potential for insecticide-treated mosquito nets to reduce malaria deaths. One recent study attempted to evaluate the impact of offering free insecticide-treated mosquito nets to families on malaria rates. As part of the evaluation a random sample of families from villages in the Nyanza Province of Kenya was divided into experimental and control groups. The control group families received free medical care and medicine and the experimental group families received free medical care and were additionally provided insecticide treated mosquito netting for their homes. The families were tracked through the course of a one year period and diagnoses of malaria were noted and study participants received appropriate treatment. One measure of malaria exposure is a simple 0-1 indicator of whether a person contracted malaria at any time over the course of the year of the study. The sample mean of this variable among the children in families who were included in the study are shown by group assignment are shown in the table below Sample Average Proportion Malaria Rates for Children by Group Assignment Group Sample Size Sample Proportion that Contracted Malaria Experimental 100 0.30 Control 100 0.45 A. What is the (population) parameter of interest in this study? In other words, what are we interested in learning about? B. Provide an estimate of the impact on having a family provided with an insecticide treated mosquito net on the incidence of malaria among children residing in the Nyanza province of Kenya. C. Construct a 90% confidence interval for the impact of providing villages in the Nyanza Province of Kenya with insecticide-treated mosquito nets on the incidence of annual malaria contraction among children. D. What would be the appropriate hypothesis to


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UW-Madison ECON 310 - homework08

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