A recent survey of 128 high school students indicated the following information about release times from school.

Question

-35 percent wanted to start school an hour eariler and get out eariler.

-20 percent liked things how they are currently

-39 percent wanted to start school an half hour later and get out later in the day.

-6 percent had no opinion.

The magein if error of this survey was calculated to be plus or minus 4 percent.

The sample size n=128

Find the interval estimates for those that want to get out eariler and those that want to get out later. Explain how it would be possible for the group that wants to get out of school eariler to win after all the votes are counted.

Answer 1

If we convert the percentages into numbers of students, including the margin of error:

Group 1: 40-49 (earlier) (31%-39%)

Group 2: 21-30 (same) (16%-24%)

Group 3: 45-55 (later) (35%-43%)

Group 4: 3-12 (no opinion) (2%-10%)

Interval estimate for group 1 is 40-49 students, and for group 3 is 45-55 students. The earlier group 1 could persuade the no opinion group 4 to join them. This would change the interval to 43-61, compared to 45-55 for group 3. In percentages this comes to 34%-47% approx.