Each person in a random sample of 1,026 adults in the United States was asked the following question. “Based on what you know about the Social Security system today, what would you like Congress and the President to do during this next year?”

The response choices and the percentages selecting them are shown below.

Completely overhaul the system: 19%

Make some major changes: 39%

Make some minor adjustments: 30%

Leave the system the way it is now: 11%

No opinion: 1%

a. Calculate a 95% confidence interval for the proportion of all United States adults who would respond “Make some major changes” to the question.

b. Give an interpretation of the confidence interval

c. Give an interpretation of the confidence level.

d. An advocate for leaving the system as it is now commented, “Based on this poll, only 39% of adults in the sample responded that they want some major changes made to the system, while 41% responded that they want only minor changes or no changes at all. Therefore, we should not change the system.” Explain why this statement, while technically correct, is misleading.