The Student Government Association wants to know if students prefer more vegetables in the daily meals at the Caf.  They decide that if two-thirds of the students who eat at the CAF want more vegetables, they will request the food service company to include more vegetables.  After surveying 100 people, they find that 70% of the sample wants more vegetables.    With a margin of error at plus or minus 10 percentage points, does the survey provide a good basis for asking the food service company to provide  more vegetables.

The Student Government Association has decided that it wants at least two-thirds or 67% to favor more vegetables before they make the request.  If 70% favors more vegetables with a margin of error of plus or minus 10, then the actual percentage of the total population favoring vegetables is between 60% and 80%.  Hence, the SGA CANNOT be confident on the basis of the survey that 67% of the students favor more vegetables.

The city of Fayetteville has a tax surplus and the mayor of the city wants to know if the citizens of Fayetteville would rather invest the surplus in a new park downtown or have a tax cut.  250 people are randomly selected from the phone book and called to check their preference.  Of the sample 60% favors a tax cut.    With a margin of plus or minus six, can the mayor safely assume that a majority favors a tax cut?

Yes, the mayor can be 95% confident that the actual number of residents favoring a tax cut is between 54% to 66%.  The lowest number in the range is still more than a majority (51%).

CNN reports that their most recent poll shows that 44% of a sample of 1000 people said they favor Candidate X for president, while 41% favor Candidate Y.  With a margin of error of plus or minus 3, can Candidate X be described as ahead in the poll?

With a margin of error of plus or minus 3, the survey tells us that the actual percentage of voters favoring Candidate X is between 41% and 47% and the percentage favoring Candidate Y is between 38% and 44%.  Since these ranges overlap, the survey does not enable us to state with confidence that either candidate is ahead of the other.

If you do a survey of 250 FSU students to determine if they want more computer laboratories available to them, what would be the minimum percentage of your sample that would have to answer in one way for you to be 95% confident that a majority of all students would answer in the same way? (Use the chart above.)

57%.  A random sample of 250 will have a margin of error of plus or minus 6, so that if a simple majority is 51%, you would have to have 57% to answer in one way to be confident that the majority held the same view.

On election day, a researcher sets up surveys at randomly selected voting locations thoughout the state.  These surveys ask voters to tell who they voted for in the governor's race.  By noon, the researcher has collected 1,000 surveys.   The surveys reveal that 52% have voted for Candidate Bigs Smile and that 45% have voted for Candidate Hearty Handshake.  Can the researcher confidently predict a winner of the race?

The researcher can say that if the voting continues at the same rate, then the Bigs Smile will win by a slight majority.  With a random sample of 1,000, the margin of error is plus or minus three.  Hence, the actual percentage of those who voted for Bigs Smile is between 49% and 55%, whereas the actual percentage of those who voted for Hearty Handshake is between 42% and 48%.  The lowest number in Bigs Smile's range is higher thant the highest number in Hearty Handshake's range.