First 5 problems of practice final exam for Sciences Po course, for mardi, 15 dec, 2009

You may use the textbook and one feuille of notes (both sides). No other references. You can use a pocket calculator but no computer.

Also please note that all these examples are fake; they are not based on real data.

Below are the first five problems; I'll send more soon.

Problem 1.

1000 people are surveyed and asked how many political activities they have done in the previous year. 300 people say “none,” 300 say “one,” 200 say “two,” 100 say “three,” and 100 say “4 or more.”

Give an estimate and standard error of the average number of political activities done by people in the population. (Hint: to compute the standard error of the mean, you need to estimate the standard distribution of the responses. If you draw a histogram of the responses, that should help.)

Problem 2.

A survey is done asking people if they support government-supplied child care. 60% of the men in the survey answer yes (with a standard error of 5%), and 70% of the women answer yes (with a standard error of 5%).

Give an estimate and standard error for the difference in support between men and women.

Assuming the data were collected using a simple random sample, how many people responded to the survey?

How large would the sample size have to be for the difference in support between men and women to have a standard error of 1%?

Problem 3.

A survey is done asking people if they support affirmative action for ethnic minorities. 30% of whites say yes (with a standard error of 3%), 80% of blacks say yes (with a standard error of 5%), and70% of others say yes (with a standard error of 10%).

The population of interest is 70% white, 20% black, and 10% other. Assuming the survey is a simple random sample, give an estimate and standard error of the percentage of people in the population who support affirmative action for ethnic minorities.

Problem 4.

1100 people are surveyed: 500 say they voted for John McCain and 600 say they voted for Barack Obama. Of the McCain voters, 40% support the health-care bill that is being debated in Congress. Of the Obama voters, 70% support the bill. (People who did not vote in the past election are excluded from this study.)

Suppose you take the data (y=1 for supporting the bill and 0 for opposing it) and run a linear regression, predicting y from a variable called “obama,” which is 1 for people who say they voted for Obama and 0 for people who say they voted for McCain.

The regression output looks like this:

lm(formula = y ~ obama)
coef.est coef.se
(Intercept) 0.__ 0.__
obama 0.__ 0.__
---
n = ____, k = _
residual sd = 0.__, R-Squared = 0.__

Fill in the blanks.

Problem 5.

Students in a laboratory experiment are given the choice of which of two video games to play, a storybook adventure or a shoot-em-up game. A logistic regression is fit predicting the students’ choice (y=0 if they choose the adventure or 1 if they choose the shooting game), given their age in years. (The students’ ages in the experiment range from 18 to 25 years.)

The logistic regression output looks like this:

glm(formula = y ~ age, family = binomial(link = "logit"))
coef.est coef.se
(Intercept) 5.64 1.61
age -0.30 0.08
---
n = 230, k = 2
residual deviance = 263.5, null deviance = 281.0 (difference = 17.4)

From this model, what is the probability of choosing the shooting game if you are 20 years old?

Graph the fitted regression line (from x ranging from 18 to 25) , and put in a bunch of dots representing values of x and y that are consistent with the fitted line.