POLS 3000 Fall 2013 STATISTICS ASSIGNMENT 2 DUE by Friday, November 1 (11:59PM) YOU MUST SHOW ALL CALCULATIONS AND DRAW THE CORRESPONDING CURVES TO RECEIVE FULL CREDIT 1. Use the individual Z-score formula (Chapter 6) to answer these questions. You may round off to the nearest Z-score (two decimal places) to figure out your answer: A survey is conducted in one U.S. state in 2013, asking 450 respondents of voting age their views about how their Senators performed on the budget impasse. One of the items in the survey asks the respondents to rate their feelings towards their junior Senator on a scale from 0 (very cold/negative) to 50 (neutral) to 100 (very positive/warm). The distribution of data is surprisingly normal. The calculated values for these 450 individuals are as follows: Mean = 45.8 degrees Standard deviation= 9.2 degrees a. What percentage of respondents gave the junior Senator a scale rating above 50 degrees (i.e., a positive rating)? b. The lowest 25% of the ratings were below what scale (degrees) score? c. What would be the lowest and highest rating that define the middle 95% of the ratings given by these 450 individuals? 2. Use the sampling mean Z-score formula (Chapter 7) to answer these questions. You may round off to the nearest Z-score (two decimal places) to figure out your answer: Let’s assume, for the sake of argument (and this assignment), that these 450 respondents are a random sample taken from the entire voting age population in that state. Use the same mean and standard deviation. a. Using 95% confidence interval tests, what would you estimate the true mean rating to be of the entire population from which this sample was randomly drawn? (The two normal curve model—see p.135—works here) b. Based on the confidence interval you calculated in question 2a, would you be able to confidently reject the possibility that 50 degrees is the true mean of the population? Why or why not? c. Would you be able to confidently reject the possibility that 45…