To determine which option correctly shows the variability in the sample proportions (\( \hat{p} \)), we need to look at the provided calculated sample proportions from the initial table. The values for \( \hat{p} \) based on the number of students who walk to school are:
- Sample 1: 6 out of 25 = \( \hat{p}_1 = \frac{6}{25} = 0.24 \)
- Sample 2: 8 out of 25 = \( \hat{p}_2 = \frac{8}{25} = 0.32 \)
- Sample 3: 7 out of 25 = \( \hat{p}_3 = \frac{7}{25} = 0.28 \)
- Sample 4: 2 out of 25 = \( \hat{p}_4 = \frac{2}{25} = 0.08 \)
- Sample 5: 5 out of 25 = \( \hat{p}_5 = \frac{5}{25} = 0.20 \)
The calculated sample proportions are as follows:
- Sample 1: 0.24
- Sample 2: 0.32
- Sample 3: 0.28
- Sample 4: 0.08
- Sample 5: 0.20
Now, we need to check the provided response options to see which one matches these values:
- One option lists \( p = 0.24, 0.32, 0.28, 0.08, 0.20 \) (This matches the calculated proportions).
- Another option provides values that are all significantly lower, indicating incorrect proportions (0.12, 0.16, etc.).
- Other options also provide inappropriate proportions.
The correct response that shows the sample proportions \( \hat{p} \) accurately is:
This table shows calculated sample proportions for students who walk to school. Sample Students in the Sample Number Who Walk to School (p^) 1 25 6 0.24 2 25 8 0.32 3 25 7 0.28 4 25 2 0.08 5 25 5 0.20 (the first option corresponds correctly to the calculated values).