In a Time Magazine/Aspen poll of American adults conducted by the strategic research firm, Penn Schoen Berland, these adults were asked, “In your opinion, what is more important for the U.S. to focus on in the next decade?” Eighty-three percent of the adults polled said domestic issues (Time, July 11, 2011). Assume that this percentage is true for the 2011 population of American adults. In a recent random sample of 1400 adults, 1078 held this opinion.
a. Using the critical-value approach and α = .01, test whether the current percentage of American adults who hold the above opinion is less than 83%.
b. How do you explain the Type I error in part a? What is the probability of making this error in part a?
c. Calculate the p-value for the test of part a. What is your conclusion if α = .01?