A student council wants to estimate the proportion of students in the school who prefer having a longer lunch period. Three different random samples of 50 students each were taken. Sample 1: 28 out of 50 prefer longer lunch. Sample 2: 31 out of 50 prefer longer lunch. Sample 3: 29 out of 50 prefer longer lunch. Based on these samples, about how much do the sample estimates vary (use the range of the sample proportions)?
- About 3 percentage points (from 58% to 61%).
- About 34 percentage points (from 28% to 62%).
- They do not vary at all because all samples come from the same school.
- About 6 percentage points (from 56% to 62%). (correct answer)
Explanation: Each proportion comes from dividing responses by sample size: 28/50 = 56%, 31/50 = 62%, and 29/50 = 58%. The range of these proportions is the highest minus the lowest, 62% minus 56% = 6 percentage points, matching choice D. Choice A's "3 percentage points, 58% to 61%" doesn't match any of the actual sample values. Saying the samples don't vary ignores that the three proportions are different, and 34 percentage points wrongly treats one of the raw counts as if it were a percentage.