Although most people are aware of minor dehydration symptoms such as dry skin and headaches, many are less knowledgeable about the causes of dehydration. According to a poll done for the Nutrition Information Center, the results of a random sample of 3003 American adults showed that 20% did not know that caffeine dehydrates. The survey listed a margin of error of plus or minus 1.8%.
a. Describe how this survey of 3003 American adults fits the properties of a binomial experiment. Specifically identify n, a trial, success, p, and x.
b. What is the point estimate for the proportion of all Americans who did not know that caffeine dehydrates? Is it a parameter or a statistic?
c. Calculate the 95% confidence maximum error of estimate for a binomial experiment of 3003 trials that result in an observed proportion of 0.20.
d. How is the maximum error, found in part c, related to the 1.8% margin of error quoted in the survey report?
e. Find the 95% confidence interval for the true proportion p based on a binomial experiment of 3003 trials that results in an observed proportion of 0.20.