Problem 3 Allcott and Gentzkow (2017) conducted an online survey of US adults regarding fake news after the 2016 presidential election. In their survey, they showed survey respondents news headlines about the 2016 election and asked about whether the news headlines were true or false. Some of the news headlines were fake and others were true. Their dependent variableY, takes value 1 if survey respondent i correctly identifies whether the headline is true or false, value 0.5 if respondent is "not sure", and value 0 otherwise. Suppose that one conducts a similar survey and obtains the following regression result: Y, - 0.65 + 0.010College + 0.015 In(Daily media time) + 0.003Age, R2 - 0.14, n = 828, (0.02) (0.004) (0.003) (0.001) where College is a binary indicator that equals 1 if a survey respondent is college graduate and 0 otherwise, In(Daily media time) is the logarithm of daily time-consuming media, and Age is age in years. a) Suppose that you would like to test that people with higher education have more accurate beliefs about news at the 1% level. State your null hypothesis precisely and report your test result. b) The estimated coefficient for In(Daily media time) is significantly positive. Interpret this result. Explain why this is plausible. c) Even if Age is omitted, there will be little concern about the omitted variable bias problem. Do you agree? Explain briefly. d) Suppose that you now conjecture that Republicans may have different beliefs about news than Democrats. Assume that there are three groups in the data: Democrats, Republicans and Independents. How would you change the specification of the linear regression model by adding or subtracting regressors? Explain briefly