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Stat401E Fall 2010 Lab 4 1. Imagine that the statistical data collected and disseminated by CBS/New York Times are based on random samples of 2000 Americans (i.e., NOT on samples of size 1068 as calculated in class). You wish to use data from one of these samples to estimate the proportion of Americans who are Catholic. If CBS/New York Times were to have collected data from 1000 samples this size (i.e., of n = 2000) in how many of these samples would you expect an estimate of the proportion of Catholics to fall into an interval that is from .03 above to .03 below the true proportion of Catholics in the U.S. population? 2. In Zimbabwe, members of a slowly emerging middle class fervently believe that once women gain the legal right to own land, women will be more likely to participate in the country's rural development. However, this belief was recently brought into question by data obtained when women members of the country's Notanku tribe were asked during a survey what they would do if the government were to give them two hectares of their own land. Only 20% of the women from the Notanku tribe indicated that they would invest in the property. Instead, each woman from the other 80% stated that she would immediately give the land to her husband, or that she would sell the property and turn over the proceeds to her husband once she married. Careful follow-up field work revealed a Notanku tribal custom that wives always give "first gifts only" to their husbands (or future husbands). Moreover, it turns out that the government had already given a "first gift" to each of the 20% of the Notanku women who were willing to invest in land that comprised for them the government's second (or subsequent) gift. You theorize that more Notanku women would invest in the two hectares of land if it were a second gift from the government. a. Initially you consider conducting face-to-face interviews with a random sample of 8 Notanku women. Your plan is to ask each woman whether or not she would invest in two hectares of land if it were her second gift from the government. If this change of wording in fact has no effect on Notanku women's responses (i.e., no effect from what was found in the earlier survey), what is the probability that all 8 women in a random sample of 8 Notanku women indicate a willingness to invest in the two hectares? b. You obtain sufficient funding to conduct face-to-face interviews with a random sample of 55 Notanku women. Your findings are that thirty-three (33) of the women responded "yes," they would invest; twenty-two (22) responded "no," they would not invest. Find a 95% 1 confidence interval for the proportion of women who responded "yes" (i.e., that they would invest). 3. Solve both of the following for k. (Hints: Assume that k is a constant. Part b has a solution for k that is a real number; part a does not. Also, you may wish to (optionally) check your solutions by substituting them back into the original equations.): n a. –kXi 3 = k 2 i=1 n k b. –3 Xi i=1 – knX = ----------------------- – --4- – k k nX n Xi i=1 2