A company that is selling condos in Florida plans to send out an advertisement for the condos to 500 potential customers, in which they promise a free weekend at a resort on the Florida coast in exchange for agreeing to attend a four-hour sales presentation. The company would like to know how many people will accept this invitation. Its best guess is that there is a 10% chance that any particular customer will accept the offer. The company decides to simulate about what proportion could actually accept the offer, if this is the case. Simulate this scenario for the company, using the Sampling Distribution web app accessible from the book’s website. Refer to Activity 1 for guidance on using the app.
a. Perform one simulation for a sample of size 500. What sample proportion did you get? Why do you not expect to get exactly 0.10?
b. Now simulate 10,000 times. Keep the sample size at n = 500 and p = 0.10. Describe the graph representing the simulated sampling distribution of the 10,000 sample proportion values. Does it seem likely that the sample proportion will fall close to 10%, say within 5 percentage points of 10%? (Note: An option in the app allows you to zoom in on the x-axis.)