Question

question 17 (4 points)
a school is going to offer a new class next year. the school polls the students to see which class they would prefer. 47% respond that they would like east asian history. 53% respond that they would like southern african studies. the margin of error for the poll is ±4%. explain whether the poll clearly indicates the majority’s preference.

Explanation:

Step1: Analyze East Asian History range

The percentage for East Asian History is 47%, with a margin of error of ±4%. So the range is \(47\% - 4\% = 43\%\) to \(47\% + 4\% = 51\%\).

Step2: Analyze Southern African Studies range

The percentage for Southern African Studies is 53%, with a margin of error of ±4%. So the range is \(53\% - 4\% = 49\%\) to \(53\% + 4\% = 57\%\).

Step3: Check for overlap

The range for East Asian History (43% - 51%) and Southern African Studies (49% - 57%) overlap between 49% and 51%. This means there's a possibility that the true percentage for East Asian History could be as high as 51% and for Southern African Studies as low as 49%, so we can't be certain that Southern African Studies is the clear majority preference.

Answer:

The poll does not clearly indicate the majority’s preference because the confidence intervals (ranges considering margin of error) for the two classes' preferences overlap. The range for East Asian History is 43% - 51% and for Southern African Studies is 49% - 57%, so there's uncertainty about which class is actually preferred by the majority.