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Solutions for Session 9, Part D
See solutions for Problems: D1 | D2 | D3 | D4 | D5 | D6
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Problem D1 | |
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There are more estimates from the distribution for sample size 20 that fall in the 4H and 5L stems (i.e., in the range 450-549). This suggests that the estimates from 20 sub-regions are more accurate.
<< back to Problem D1
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Problem D2 | |
a. | Here is the completed table: |
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Interval |
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Interval Length |
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Proportion of Estimates in Interval |
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Sample Size 10 |
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Sample Size 20 |
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350-650 |
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300 |
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100/100 |
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100/100 |
375-625 |
250 |
98/100 |
100/100 |
400-600 |
200 |
94/100 |
98/100 |
425-575 |
150 |
84/100 |
94/100 |
450-550 |
100 |
69/100 |
83/100 |
475-525 |
50 |
37/100 |
55/100 |
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b. | Each interval of the samples of 20 sub-regions contains a higher proportion of estimates. For instance, the interval 450-550 contains 83/100 samples of size 20, compared to 69/100 samples of size 10. A higher proportion of the estimates falls within 50 penguins of the actual population size (500) when samples of size 20 were used. This suggests that the increased sample size has a significant effect on the accuracy of the estimates. |
<< back to Problem D2
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Problem D3 | |
a. | The median is in position (100 + 1)/2 = 50.5, so it is the average of the 50th and 51st values in the ordered list. Each of these values is 500. |
b. | The quartiles will be at position (50 + 1)/2 = 25.5, so they are the average of the 25th and 26th values in their respective halves. |
c. | Here is the completed table: |
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Sample Size 10 |
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Maximum |
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620 |
Upper Quartile (Q3) |
540 |
Median |
500 |
Lower Quartile (Q1) |
470 |
Minimum |
360 |
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<< back to Problem D3
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Problem D4 | |
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Here is the completed table:
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Sample Size 20 |
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Maximum |
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610 |
Upper Quartile (Q3) |
530 |
Median |
500 |
Lower Quartile (Q1) |
482.5 |
Minimum |
390 |
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<< back to Problem D4
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Problem D6 | |
a. | The sample-to-sample variation goes down as the sample size increases. This is exhibited by the shrinking box portion of the graphs. |
b. | The estimates are closer to the actual value as the sample size increases. Both the range and the interquartile range decrease significantly from the estimates using sample size 10 and sample size 20. |
<< back to Problem D6
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