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(1) A recent poll by the Texas Tribune asked 996 Texas voters whether they would support Beto O'Rourke or Greg Abbott for governor . 552

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(1) A recent poll by the Texas Tribune asked 996 Texas voters whether they would support Beto O'Rourke or Greg Abbott for governor . 552 of these voters said they supported Abbott and 444 said they supported O'Rourke (these numbers drop respondents who were undecided or planned to vote for another candidate ,but we'll ignore that in our analyses below ). (a) Based on this poll , what is your estimate of the proportion of Texas voters who support Abbott (b) Form a 95% confidence interval for this estimate. (c) Form a 99% confidence interval for this estimate. (d) Conduct a hypothesis test at the .05 signicance level to assess whether Abbott really has a majority or whether the election could be tied. Be sure to formally specify your hypotheses , show the steps of your calculation and explain briefly what your result tells you about the can- didates' support in the population. (2) A nationally representative survey of American adults, respondents were asked if they knew which party controlled the US. Senate .Out of the large sample of 6,454 respondents ,3,680 correctly said Democrats had a majority in the U.S. House of Representatives (a) Construct a 95% condence interval for the proportion of the American adult population that knew which party controlled the House. (b) Out of 2488 Democrats in the sample , 1064 correctly identied the party that controls the House . Out of 1530 Republicans in the sample ,585 correctly identied the party that controls the House .Conduct a hypothesis test at the .05 signicance level to assess whether the propor - tions of Democrats and Republicans knowing the correct answer to this question are the same . Be sure to clearly specify your null and alternative hypotheses, show the steps of your calcu lation and explain briey what your result tells you about partisans 'knowledge on this question (3) In a research paper by UT Economics professor Dan Hammermesh ,data on course instructor sur veys for 463 UT courses is analyzed. In each course, the overall instructor rating is noted. Here we'll consider differences in these ratings based on the gender of the instructor .Previous work has established strong evidence of gender bias in these sorts of ratings (here we'll only consider whether there are differences in average ratings by gender which, on its own, isn't evidence of bias, but could be consistent with it)

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