Economics 140A
Homework 1
This homework should be completed with Stata. When submitting your homework, copy-paste your Stata code at the bottom of the document you submit. You will learn how to use Stata in section.
The data set background_survey contains the answers you and your classmates gave to some of the questions in the background survey. Gender is a variable equal to 1 for females and to 0 for males. Job is a variable equal to 1 for students who have a job and to 0 for students who do not. IV_weekend_safety_fee is a variable equal to 1 for students in favor of increasing tuition fees by 50 dollars to implement new security measures and ensure Isla Vista (IV) is safer during weekends, and to 0 for students who answered they were against this idea. Non_response is a variable equal to 1 for students who said they would not have answered the survey if answering had not been worth 4% of the final grade, while this variable is equal to 0 for students who said they would still have answered.
The students who answered the question about the increase in tuition fees to implement more safety measures in IV were randomly divided into 10 groups of equal size. The number of the group a student is assigned to is in the variable randomdraw, which takes values from 1 to 10. Each group of students with the same value of the variable randomdraw is a random sample of size n drawn without replacement from the total population of N students who answered this question.
1. Among those who answered the question (N students), what is the percentage of your classmates in favor of increasing tuition fees by 50 dollars to implement new security measures and ensure Isla Vista is safer during weekends? Hereafter, let p denote that number.
2. Compute the percentage of students in favor of increasing tuition fees to implement security measures in IV, in the first random sample of students (those with randomdraw=1). This percentage is your estimate of p based on the first random sample and is denoted ,1 . Is this percentage equal to the percentage of students in favor of that idea in the entire population?
3. Compute the percentage of students in favor of this measure in the 9 other random samples. Let ,2, … , ,10 denote the estimates of p based on random samples 2 through 10 (note: these are defined by the variable randomdraw). Compute , the variance of those 10 numbers.
4. According to what we saw in lecture, the variance of p(^)n is equal to (the additional term comes from the fact the sample is drawn without replacement). Given the value of p you found in question 1, compute that number. Is the number you found very far from the number you found in question 3? Explain.
5. For each of the 10 samples of students, compute the 95% confidence interval for p according to the formula we saw during lecture, and assess whether p indeed belongs to that interval. For what proportion of these 10 samples does p indeed belong to the confidence interval? Does that make sense? Explain your answer.
6. Compare the percentage of students in favor of increasing tuition fees to implement new security measures in IV among male and among female students. Is the difference between the two groups statistically significant at the 5% level? Hint: you can use the Stata command regress.
7. Compare the percentage of students in favor of increasing tuition fees to implement new security measures in IV, among students with a job and students without a job. Is the difference between the two groups statistically significant at the 5% level? Hint: you can use the Stata command regress. If the difference is statistically significant, try to explain what causes this difference.
8. When asked whether they would have answered the survey if it had not been worth 4% of the final grade, those who said they would still have replied are coded Non_response=0, while those who said they would not have replied are coded Non_response=1. The first group consists of students who answer surveys even if they do not have an incentive to do so, so let's call them always respondents. The second group consists of students who only answer surveys if they have an incentive to do so, so let's call them incentivized respondents. If there had not been an incentive to answer this survey, only the always respondents would have answered. What would the response rate have been in this case? Compare the percentage of females among the always respondents and to the percentage of females among the incentivized respondents. Is the difference between the two groups statistically significant at the 5% level? Hint: you can use the Stata command regress.
9. Compare the percentage of students in favor of increasing tuition fees to implement new security measures in IV among the always respondents and the incentivized respondents. Is the difference between the two groups statistically significant at the 5% level? Hint: you can use the Stata command regress.
10. Assume the university wants to know whether it should increase tuition fees by 50 dollars to implement new security measures in IV. To make that decision, they will survey students, and they will implement this measure if more than 50% of the students that respond to their survey are in favor of this idea. Only the always respondents will respond to the survey, because there is no incentive to respond. Do you think that the results of the survey can give the university a reliable measure of whether more or less than 50% of students are in favor of that idea? Hint: use the result from the previous question.