Use the accompanying paired data consisting of registered boats? (tens of? thous
ID: 2947648 • Letter: U
Question
Use the accompanying paired data consisting of registered boats? (tens of? thousands) and manatee fatalities from boat encounters. Let x represent the number of registered boats and let y represent the corresponding number of manatee deaths. Use the given number of registered boats and the given confidence level to construct a prediction interval estimate of manatee deaths. Use = 87 (for 87?0,000 registered? boats) with a 99?% confidence level.
Find the indicated prediction interval.
__ manatees < y < __ manatees
Boats
?(tens of? thousands)
Manatees
65
51
70
38
66
36
72
51
69
41
70
58
75
55
82
65
85
83
87
80
92
82
95
96
91
73
97
69
98
80
100
90
97
72
99
92
95
97
88
84
89
89
85
81
90
71
88
70
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?(tens of? thousands)
Manatees
65
51
70
38
66
36
72
51
69
41
70
58
75
55
82
65
85
83
87
80
92
82
95
96
91
73
97
69
98
80
100
90
97
72
99
92
95
97
88
84
89
89
85
81
90
71
88
70
Explanation / Answer
The statistical software output for this problem is:
Simple linear regression results:
Dependent Variable: Manatees
Independent Variable: Boats
Manatees = -46.112894 + 1.3744301 Boats
Sample size: 24
R (correlation coefficient) = 0.85874173
R-sq = 0.73743737
Estimate of error standard deviation: 9.5288474
Parameter estimates:
Analysis of variance table for regression model:
Predicted values:
Hence,
99% prediction interval will be:
46.035 < y < 100.890
Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept -46.112894 15.025093 ? 0 22 -3.0690589 0.0056 Slope 1.3744301 0.17484982 ? 0 22 7.8606318 <0.0001Related Questions
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