To do these exercises, go to www.macmillanhighered.com/fapp10e.

Question 7.104

3. Suppose that 60% of the population bought a lottery ticket in the last 12 months. (This is the setting for Exercise 51.) You can use the Probability applet to simulate the behavior of random samples of size 50 from this population. You want to take many samples from this population to observe how the sample proportion that plays the lottery varies from sample to sample. By moving the sliders, specify the “Probability of Heads” setting in the applet as 0.6 and the number of tosses as 50. This simulates an SRS of size 50 from a large population. Each head in the sample is a person who plays the lottery, and each tail is a person who does not play. By alternating between “Toss” and “Reset,” you can take many samples quickly.

  1. Take 25 samples, recording the proportion in each sample that plays the lottery. (The applet gives this proportion at the top left of its display.) Make a histogram of the 25 sample proportions.
  2. Another population contains only 20% of people who play the lottery. Take 25 samples of size 50 from this population, record the number in each sample that plays, and make a histogram of the 25 sample proportions. How do the centers of your two histograms reflect the differing truths about the two populations?