Simulate some coin tosses. The Probability applet simulates tossing a coin, with the advantage that you can choose the true long-term proportion, or probability, of a head. Example 3.30 discusses sampling from a population in which proportion p = 0.6 (the parameter) ate in a restaurant during the past week. Tossing a coin with probability p = 0.6 of a head simulates this situation: each head is a person who ate at a restaurant during the past week, and each tail is a person who did not. Set the “Probability of heads” in the applet to 0.6 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 only20%who ate at a restaurant in the past week. Take 50 samples of size 25 from this population, record the number in each sample who ate at a restaurant in the past week, and make a histogram of the 50 sample proportions.

How do the centers of your two histograms reflect the differing truths about the two populations?