CH ALLENGE Use the statistical software for simulations. Statistical software can speed simulations. We are interested in the sampling distribution of the proportion p of

CH ALLENGE Use the statistical software for simulations. Statistical software can speed simulations. We are interested in the sampling distribution of the proportion ˆp of people who find shopping frustrating in an SRS from a population in which proportion p find shopping frustrating.

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.

For example, in CrunchIt! go to “Simulate data” in the “Data” menu, and choose “Binomial.”

(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 finds shopping frustrating. 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 find shopping frustrating. 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?