Use the table to answer the question.

Question

Sample Students in the Sample Number Who Walk to School
1 25 6
2 25 8
3 25 7
4 25 2
5 25 5 For a class project, you take five different samples of students and ask them whether they walk to school. The data is consolidated in the preceding table. Which of the following correctly shows the variability in the sample proportions (p^)?
Responses

Sample Students in the Sample Number Who Walk to School (p^)
1 25 6 0.12
2 25 8 0.16
3 25 7 0.14
4 25 2 0.04
5 25 5 0.10 Sample Students in the Sample Number Who Walk to School (p^)
1 25 6 0.12 2 25 8 0.16 3 25 7 0.14 4 25 2 0.04 5 25 5 0.10 - incorrect

Sample Students in the Sample Number Who Walk to School (p^)
1 25 6 0.06
2 25 8 0.08
3 25 7 0.07
4 25 2 0.02
5 25 5 0.05 Sample Students in the Sample Number Who Walk to School (p^)
1 25 6 0.06 2 25 8 0.08 3 25 7 0.07 4 25 2 0.02 5 25 5 0.05 - incorrect

Sample Students in the Sample Number Who Walk to School (p^)
1 25 6 0.18
2 25 8 0.24
3 25 7 0.21
4 25 2 0.06
5 25 5 0.20 Sample Students in the Sample Number Who Walk to School (p^)
1 25 6 0.18 2 25 8 0.24 3 25 7 0.21 4 25 2 0.06 5 25 5 0.20 - incorrect

Sample Students in the Sample Number Who Walk to School (p^) - correct
1 25 6 0.24
2 25 8 0.32
3 25 7 0.28
4 25 2 0.04
5 25 5 0.20

explain how you get the correct answer in 2 sentences.

Answer 1

The correct answer is the last option where the sample proportions (p^) are calculated by dividing the number who walk to school by the total number of students in the sample. This results in the variation in the sample proportions reflecting the true variability in the data.