On January 4. 2000, the Gallup Organization released the results of a poll dealing with the likelihood of computer-related Y2K problems and the possibility of terrorist attacks during the New Year's holiday at the turn of the century.7 The survey results were based on telephone interviews with a randomly selected national sample of 622 adults, 18 years and older, conducted December 28, 1999.
a. The Gallup poll found that 61 percent of the respondents believed that one or more terrorist attacks were likely to happen on the New Year's holiday. Based on this finding, calculate a 95 percent confidence interval for the proportion of all U.S. adults who believed that one or more terrorist attacks were likely to happen on the 2(KK) New Year's holiday. Based on this interval, is it reasonable to conclude that fewer than two-thirds of all U.S. adults believed that one or more terrorist attacks were likely?
b. In explaining its survey methods, Gallup states the following: "For results based on this sample, one can say with 95 percent confidence that the maximum error attributable to sampling and other random effects is plus or minus 4 percentage points." Explain how your calculations for part a verify that this statement is true.