Question: On September 10, 1998, the "Starr Report," alleging impeachable offenses by President Bill Clinton, was released to Congress. That evening, the Gallup Organization conducted a poll of 645 adults nationwide to assess initial reaction (reported at www.gallup.com). One of the questions asked was: "Based on what you know at this point, do you think that Bill Clinton should or should not be impeached and removed from office?" The response "Yes, should" was selected by 31% of the respondents.
a. The Gallup Web page said, "For results based on the total sample of adults nationwide, one can say with 95% confidence that the margin of sampling error is no greater than ±4 percentage points." Explain what this means and verify that the statement is accurate.
b. Give a 95% confidence interval for the proportion of all adults who would have said President Clinton should be impeached had they been asked that evening.
c. A similar Gallup Poll taken in early June 1998 found that 19% responded that President Clinton should be impeached. Do you think the difference between the results of the two polls can be attributed to chance variation in the samples taken, or does it represent a real difference of opinion in the population in June versus mid-September? Explain.