Problem Set
1. In the most recent presidential election, the polling firm Smith & Brady predicted that the Republican candidate would receive 54% of the popular vote and the Democratic candidate would receive 46% of the popular vote. On Election Day, the Republican candidate received 47% of the vote and the Democratic candidate received 53% of the vote. Describe a scenario in which Smith & Brady overestimated the Republican candidate's vote share because of selection bias. In other words, explain how this could have happened.
2. Suppose that the average educational attainment (in years) for 163 countries (almost all countries in the world) is distributed normally with a mean of 7.3 and a standard deviation of 2.8: educational attainment ~ N(μ=7.3, σ=2.8).
a. What is the probability that a randomly selected country will have an average educational attainment between five years and eight years?Hint: to answer this question, you can either use R or the standard normal table (Table 6-3 in Pollock).
b. What is the probability that a randomly selected country will have an average educational attainment above 12 years?
Hint: to answer this question, you can either use R or the standard normal table (Table 6-3 in Pollock).
3. A recent survey conducted by the Pew Research Center measured support in the American public for laws that would permit illegal immigrants to remain in the country. Approximately 72% of the 1,103 respondents expressed support for permitting illegal immigrants to stay whereas 28% expressed opposition to this proposed reform.
a. What is the standard error of the percentage of respondents who support the proposed reform?
b. What is the 95% confidence interval for the percentage of respondents who support the proposed reform?
4. For this question, you will use the world.csv dataset.
The Organisation for Economic Cooperation and Development (OECD) was founded in 1961 to promote trade and economic progress. Member countries are all committed to maintaining a democratic system of government and free market. The OECD currently has 34 member countries.
For the problems in this section, you will compare sample means to investigate whether membership in the OECD is, in fact, associated with economic prosperity.
Use the world.csv dataset to test the argument that, in a comparison of countries, OECD countries are likely to have a higher level of economic prosperity.
To test this argument, use the following variables:
oecd: = 1 if the country is an oecd country, = 0 if the country is not an oecd country
gdp_10_thou: GDP per capita in 10K US dollars
a. State the null and alternative hypothesis.
b. Perform the necessary calculations. You should arrive at a difference in means and a standard error of this difference in means. Do this "by hand" (though you can use R) and show your work below. Don't use the t.test command.
c. Calculate a 95% confidence interval for the difference in means.
d. Calculate the test statistic for the difference in means.
e. Determine whether we should reject or fail to reject the null hypothesis at the 5% significance level based on the test statistic.
f. Perform this same hypothesis test using the t.test command in R. Copy and paste the output into your problem set. Use the results to check your work earlier work.
g. State the result of the hypothesis test in prose. In a few sentences, answer the question of whether OECD member countries are more likely to experience economic prosperity than non-OECD countries.
h. Do you think this analysis excludes important variables? In other words, are there other variables that influence the relationship between OECD membership and economic prosperity? Provide an example of one of these variables and explain.
Attachment:- Data.rar