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A survey of voters in ”Frontline” counties, counties that represent highly contested regions for congressional races, contacted a total of 1000 voters. Poll respondents were split in half, and each half was asked different questions. 322 of 500 respondents agreed with ”Making community college tuition-free for all”. 341 of 500 respondents agree with ”Making community college tuition-free for families with incomes below $125,000 a year”. We wish to test the hypothesis that the percentage of voters in frontline districts supporting free community college for lower income families is higher than the percentage supporting free community college for all families. Specifically, we test against the alternative plowerincome − pall > 0. Note that these questions should be solved using a normal approximation, not the exact or continuity corrected solutions provided by prop.test. a) If we don’t assume the two proportions are the same, what is our best estimate of the standard error of the difference between these two proportions? Save your answer in the variable q3.a b) Using the estimate of the standard error found above, calculate a 95% confidence interval for the difference between the percentage supporting free community college for lower income families and the percentage sup- porting free community college for all families. (Specifically calculate a CI for plowerincome − pall). Save your answer in the variable q3.b c) Under the assumption needed for our hypothesis test, we can calculate a more accurate estimate of the standard error of the difference between the two proportions; calculate that value. Save your answer in the variable q3.c d) Calculate the test statistic Z for this hypothesis test. Save your answer in the variable q3.d e) Calculate the p-value for this hypothesis test. Save your answer in the variable q3.e f) TRUE or FALSE, testing at a 5% level, we can reject the alternative that a higher proportion of voters support free community college for lower income families than support free community college for all families. Save your answer in the variable q3.f