“You say tomato, burger lovers say ketchup!” According to a recent T.G.I. Friday’s restaurants’ random survey of 1027 Americans, approximately half (47%) said that ketchup is their preferred burger condiment. The survey quoted a margin of error of plus or minus 3.1%.
a. Describe how this survey of 1027 Americans 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 prefer ketchup on their burger? Is it a parameter or a statistic?
c. Calculate the 95% confidence maximum error of estimate for a binomial experiment of 1027 trials that results in an observed proportion of 0.47.
d. How is the maximum error, found in part c, related to the 3.1% 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 1027 trials that results in an observed proportion of 0.47.