Generating a sampling distribution. We want to know what percent ofAmerican adults

Chapter 0, Problem 11.43

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Generating a sampling distribution. We want to know what percent ofAmerican adults approve of legal gambling. This population proportion p is aparameter. To estimate p, take an SRS and find the proportion p in the samplewho approve of gambling. If we take many SRSs of the same size, the proportionp will vary from sample to sample. The distribution of its values in all SRSs is thesampling distribution of this statistic.Jeff Greenberg/The Image WorksFigure 11.10 is a small population. Each circle represents an adult. The coloredcircles are people who disapprove of legal gambling, and the white circles arepeople who approve. You can check that 60 of the 100 circles are white, so in thispopulation the proportion who approve of gambling is p = 60/100 = 0.6.(a) The circles are labeled 00, 01, . . . , 99. Use line 101 of Table B to draw an SRSof size 5. What is the proportion p of the people in your sample who approve ofgambling?(b) Take 9 more SRSs of size 5 (10 in all), using lines 102 to 110 of Table B, adifferent line for each sample. You now have 10 values of the sample proportionp. What are they?(c) Because your samples have only 5 people, the only values p can take are 0/5,1/5, 2/5, 3/5, 4/5, and 5/5. That is, p is always 0, 0.2, 0.4, 0.6, 0.8, or 1. Mark thesenumbers on a line and make a histogram of your 10 results by putting a bar aboveeach number to show how many samples had that outcome. (You have begun toconstruct the sampling distribution of p, although just 10 samples is a small start.)(d) Taking samples of size 5 from a population of size 100 is not a practicalsetting, but lets look at your results anyway. How many of your 10 samplesestimated the population proportion p = 0.6 exactly correctly? Is the true value0.6 roughly in the center of your sample values?