Baseball fans. In a poll taken in March of 2007, Gallup asked 1006 national adults whether they were baseball fans. 36% said they were. A year previously, 37% of a similar-size sample had reported being baseball fans.

a) Find the margin of error for the 2007 poll if we want 90% confidence in our estimate of the percent of national adults who are baseball fans.

b) Explain what that margin of error means.

c) If we wanted to be 99% confident, would the margin of error be larger or smaller? Explain.

d) Find that margin of error.

e) In general, if all other aspects of the situation remain the same, will smaller margins of error produce greater or less confidence in the interval?

f) Do you think there's been a change from 2006 to 2007 in the real proportion of national adults who are baseball fans? Explain.