Concept explainers
(a)
To find: 95% confidence interval for the mean diameter of the species.
(a)
Answer to Problem 10.79SE
A 95% confidence interval gives the upper and lower limits for
Explanation of Solution
Given:
Specimen | Diameter | Height | D/H |
OSU 36651 | 185 | 78 | 2.37 |
OSU 36652 | 194 | 65 | 2.98 |
OSU 36653 | 173 | 77 | 2.25 |
OSU 36654 | 200 | 76 | 2.63 |
OSU 36655 | 179 | 72 | 2.49 |
OSU 36656 | 213 | 76 | 2.80 |
OSU 36657 | 134 | 75 | 1.79 |
OSU 36658 | 191 | 77 | 2.48 |
OSU 36659 | 177 | 69 | 2.57 |
OSU 36660 | 199 | 65 | 3.06 |
184.5 | 73 | 2.54 | |
S: | 21.5 | 5 | .37 |
Calculation:
For the Diameter of the Species:
The sample mean and standard deviation for the recorded data are,
If you choose a 5% level of significance (
A 95% confidence interval gives the upper and lower limits for
Thus, you can estimate with 95% confidence that the average diameter lies between
Conclusion: Thus, a 95% confidence interval gives the upper and lower limits for
(b)
To find: a 95% confidence interval for the mean height of the species.
(b)
Answer to Problem 10.79SE
A 95% confidence interval gives the upper and lower limits for
Explanation of Solution
Given:
Specimen | Diameter | Height | D/H |
OSU 36651 | 185 | 78 | 2.37 |
OSU 36652 | 194 | 65 | 2.98 |
OSU 36653 | 173 | 77 | 2.25 |
OSU 36654 | 200 | 76 | 2.63 |
OSU 36655 | 179 | 72 | 2.49 |
OSU 36656 | 213 | 76 | 2.80 |
OSU 36657 | 134 | 75 | 1.79 |
OSU 36658 | 191 | 77 | 2.48 |
OSU 36659 | 177 | 69 | 2.57 |
OSU 36660 | 199 | 65 | 3.06 |
184.5 | 73 | 2.54 | |
S: | 21.5 | 5 | .37 |
Calculation:
For the Height of the Species:
The sample mean and standard deviation for the recorded data are,
A 95% confidence interval gives the upper and lower limits for
Thus, you can estimate with 95% confidence that the average height lies between
Conclusion: Thus, a 95% confidence interval gives the upper and lower limits for
(c)
To find: a 95% confidence interval for the mean ratio of diameter to height.
(c)
Answer to Problem 10.79SE
A 95% confidence interval for the mean ratio of diameter to height is
Explanation of Solution
Given:
Specimen | Diameter | Height | D/H |
OSU 36651 | 185 | 78 | 2.37 |
OSU 36652 | 194 | 65 | 2.98 |
OSU 36653 | 173 | 77 | 2.25 |
OSU 36654 | 200 | 76 | 2.63 |
OSU 36655 | 179 | 72 | 2.49 |
OSU 36656 | 213 | 76 | 2.80 |
OSU 36657 | 134 | 75 | 1.79 |
OSU 36658 | 191 | 77 | 2.48 |
OSU 36659 | 177 | 69 | 2.57 |
OSU 36660 | 199 | 65 | 3.06 |
184.5 | 73 | 2.54 | |
S: | 21.5 | 5 | .37 |
Calculation:
For the ratio of diameter to height of the species:
The sample mean and standard deviation for the recorded data are,
A 95% confidence interval gives the upper and lower limits for
Conclusion: Thus, a 95% confidence interval for the mean ratio of diameter to height is
(d)
To compare:the intervals found in parts a, b, and c and explain whether the average of the ratios is same as the ratio of the average diameter to average height
(d)
Answer to Problem 10.79SE
The average of the ratios is same as the ratio of the average diameter to average height.
Explanation of Solution
Calculation:
The width of the interval for the mean diameter of the species is wider than the other two intervals because of its larger standard deviation.
Since, the difference is very low we can assume that both are equal.
Conclusion: Thus, the average of the ratios is same as the ratio of the average diameter to average height.
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Chapter 10 Solutions
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