Question

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

- 35 percent wanted to start school a hour earlier and get out earlier
- 20 percent liked things how they are currently
- 39 percent wanted to start school a half an hour later and get out later in the day
- 6 percent had no opinion

The margin of error for this survey was calculated to be plus or minus 4 percent
The sample size is n=128
Find the interval estimates for those that want to get out earlier and those that want to get out later. Explain how it would be possible for the group that wants to get out of school earlier to win after all the votes are counted.
PLEASE HELP ASAP, and show work an all steps as well. Thank you

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.