Question II In a 1994 research paper, two economists examined the impact of looks on earn- ings using interviewers' ratings of respondents' physical appearance. They used data in which respondents reported their wages, and the interviewers rated the respondent's appearance, using five categories: (1. homely, 2. quite plain, 3. average, 4. good looking and 5. strikingly hand- some or beautiful). Download the file beauty.xls from the course web page. The file contains the following variables: hourly earning, looks, female (is equal to 1 if female, 0 otherwise) and years of education. Assume that a population consists of all individuals in the data set. (a) Estimate the following regression ernhra+x looks+yx yrseduc + u (1) using the population data (i.e., use all data). What is the value of (the estimated) ? Denote this value as Bo. (b) (i) Draw a simple random sample of size 100. (ii) Estimate (1) using the sample you obtained. (iii) Test the null hypothesis Ho= Bo against H o using a = : 10% as the size of the test. Let reject be a dummy variable indicating whether Ho is rejected (reject-1 if Ho is rejected). (iv) Save BOLS, its robust standard error, and the dummy variable reject to a Stata data set, say mydata.dta. The data set contains three variables, say beta_hat, se_hat, reject (You can use your own favorite names for the data set and the variables). (c) Repeat (b) 1000 times. (d) Now load the Stata data set mydata.dta into Stata and graph the histogram of beta_hat. Is it close to be normal? (e) Summarize all variables. Is the mean of reject close to be 10%? Is your answer expected? Can you explain why or why not? (f) Is the standard deviation of beta_hat close to the mean of se_hat? Is your answer expected? Can you explain why or why not?