5.7 Constructing sampling distributions. The Probability applet simulates tossing a coin, with the advantage that you can choose the true long-term proportion, or probability, of a head. Suppose that we have a population in which proportion p=0.4 (the parameter) plan to vote in the next election. Tossing a coin with probability p=0.4 of a head simulates this situation: each head is a person who plans to vote, and each tail is a person who does not. Set the “Probability of heads” in the applet to 0.4 and the number of tosses to 25. This simulates an SRS of size 25 from this population. By alternating between “Toss” and “Reset,” you can take many samples quickly.

a. Take 50 samples, recording the number of heads in each sample. Make a histogram of the 50 sample proportions (count of heads divided by 25). You are constructing the sampling distribution of this statistic.

b. Another population contains only 15% who plan to vote in the next election. Take 50 samples of size 25 from this population, record the number in each sample who approve, and make a histogram of the 50 sample proportions.