Question

Sampling Variability in the Sample Proportion Quick Check
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Question
Use the image to answer the question.

A histogram is titled Sampling Distributions of Sample Proportions of a Population.
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Which of the following frequency tables corresponds to the histogram?

(1 point)
Responses

This table shows the sample proportions data for comparison with the histogram.
Sample Number Sample Proportion
1 0.8
2 0.78
3 0.78
4 0.86
5 0.89
6 0.47
7 0.86
8 0.69
9 0.53
10 0.62
Table with 2 columns and 11 rows.Row 1: Column 1, 'Sample Number'; Column 2, 'Sample Proportion' Row 2: Column 1, '1'; Column 2, '0.8' Row 3: Column 1, '2'; Column 2, '0.78' Row 4: Column 1, '3'; Column 2, '0.78' Row 5: Column 1, '4'; Column 2, '0.86' Row 6: Column 1, '5'; Column 2, '0.89' Row 7: Column 1, '6'; Column 2, '0.47' Row 8: Column 1, '7'; Column 2, '0.86' Row 9: Column 1, '8'; Column 2, '0.69' Row 10: Column 1, '9'; Column 2, '0.53' Row 11: Column 1, '10'; Column 2, '0.62'

This table shows the sample proportions data for comparison with the histogram.
Sample Number Sample Proportion
1 0.8
2 0.78
3 0.78
4 0.86
5 0.89
6 0.47
7 0.36
8 0.69
9 0.53
10 0.62
Table with 2 columns and 11 rows.Row 1: Column 1, 'Sample Number'; Column 2, 'Sample Proportion' Row 2: Column 1, '1'; Column 2, '0.8' Row 3: Column 1, '2'; Column 2, '0.78' Row 4: Column 1, '3'; Column 2, '0.78' Row 5: Column 1, '4'; Column 2, '0.86' Row 6: Column 1, '5'; Column 2, '0.89' Row 7: Column 1, '6'; Column 2, '0.47' Row 8: Column 1, '7'; Column 2, '0.36' Row 9: Column 1, '8'; Column 2, '0.69' Row 10: Column 1, '9'; Column 2, '0.53' Row 11: Column 1, '10'; Column 2, '0.62'

This table shows the sample proportions data for comparison with the histogram.
Sample Number Sample Proportion
1 0.8
2 0.78
3 0.78
4 0.86
5 0.89
6 0.47
7 0.86
8 0.69
9 0.53
10 0.92
Table with 2 columns and 11 rows.Row 1: Column 1, 'Sample Number'; Column 2, 'Sample Proportion' Row 2: Column 1, '1'; Column 2, '0.8' Row 3: Column 1, '2'; Column 2, '0.78' Row 4: Column 1, '3'; Column 2, '0.78' Row 5: Column 1, '4'; Column 2, '0.86' Row 6: Column 1, '5'; Column 2, '0.89' Row 7: Column 1, '6'; Column 2, '0.47' Row 8: Column 1, '7'; Column 2, '0.86' Row 9: Column 1, '8'; Column 2, '0.69' Row 10: Column 1, '9'; Column 2, '0.53' Row 11: Column 1, '10'; Column 2, '0.92'

This table shows the sample proportions data for comparison with the histogram.
Sample Number Sample Proportion
1 0.8
2 0.78
3 0.78
4 0.86
5 0.56
6 0.47
7 0.86
8 0.69
9 0.53
10 0.62
Table with 2 columns and 11 rows.Row 1: Column 1, 'Sample Number'; Column 2, 'Sample Proportion' Row 2: Column 1, '1'; Column 2, '0.8' Row 3: Column 1, '2'; Column 2, '0.78' Row 4: Column 1, '3'; Column 2, '0.78' Row 5: Column 1, '4'; Column 2, '0.86' Row 6: Column 1, '5'; Column 2, '0.56' Row 7: Column 1, '6'; Column 2, '0.47' Row 8: Column 1, '7'; Column 2, '0.86' Row 9: Column 1, '8'; Column 2, '0.69' Row 10: Column 1, '9'; Column 2, '0.53' Row 11: Column 1, '10'; Column 2, '0.62'
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Answer 1

Answer: the first table (Sample 1–10 proportions = 0.80, 0.78, 0.78, 0.86, 0.89, 0.47, 0.86, 0.69, 0.53, 0.62).

Reason: the histogram’s bar heights and locations (two values near 0.78, two near 0.86, one near 0.89, one around 0.69, one around 0.62, one around 0.53 and one low value ~0.47) match that set of sample proportions.