Use statistical software for simulations. Statistical software can speed simulations. We are interested in the sampling distribution of the proportion p of people who ate

Use statistical software for simulations. Statistical software can speed simulations. We are interested in the sampling distribution of the proportion ˆp of people who ate at a restaurant during the past week in an SRS from a population in which proportion p ate at a restaurant during the past week. Here, p is a parameter and ˆp is a statistic used to estimate p. We will see in Chapter 5 that “binomial” is the key word to look for in the software menus.

(a) Set n = 50 and p = 0.6 and generate 100 binomial observations.

These are the counts for 100 SRSs of size 50 when 60%

of the population ate at a restaurant in the past week. Save these counts and divide them by 50 to get values of ˆp from 100 SRSs.

Make a stemplot of the 100 values of ˆp.

(b) Repeat this process with p = 0.3, representing a population in which only 30% of people ate at a restaurant during the past week. Compare your two stemplots. How does changing the parameter p affect the center and spread of the sampling distribution?

(c) Now generate 100 binomial observations with n = 200 and p = 0.6. This simulates 100 SRSs, each of size 200. Obtain the 100 sample proportions ˆp and make a stemplot. Compare this with your stemplot from (a). How does changing the sample size n affect the center and spread of the sampling distribution?