Recently, the Gallup Organization reported that the proportion of adult Americans aged 18 years or older who believe the state of moral values in the country is getting worse is 0.77. There are approximately 241,000,000 Americans aged 18 years or older in the United States.
(a) Now simulate obtaining at least 2000 more simple random samples of size 400 from the population. Based on the simulation, what is the probability of obtaining a random sample where the proportion of those who believe the state of moral values in the country is getting worse is greater than 0.8? Would it be unusual to obtain a sample proportion greater than 0.8 from this population? Explain.
(b) Repeat parts (a) through (c) using a sample of size 800. Comment on the role sample size plays in the variability of outcomes. What law does this illustrate?