One of the more popular statistics reported in the media is the president’s job approval rating. The approval rating is reported as the proportion of Americans who approve of the job that the sitting president is doing and is typically based on a random sample of registered voters.

(a) This proportion tends to fluctuate from week to week. Name some reasons for the fluctuation in the statistic.

(b) A recent article had the headline “Obama Ratings Rise.” This headline was written because a December 2010 poll showed President Obama’s approval rating to be 0.48 (48%). A poll the following January based on 1500 randomly selected Americans showed that 747 approved of the job Obama was doing. Do the results of the January poll indicate that the proportion of Americans who approve of the job Obama is doing is significantly higher than December’s level? Explain.