Consider the following data on x = rainfall volume (m³) and y = runoff volume (m³) for a particular location. X 4 12 14 17 23 30 40 47 55 67 72 82 96 112 127 y 4 10 13 15 15 25 27 46 38 46 53 70 82 99 100 Use the accompanying Minitab output to decide whether there is a useful linear relationship between rainfall and runoff. The regression equation is runoff = -0.97 +0.824 rainfall Coef -0.971 0.82401 s = 5.211 R-sq = 97.6% State the appropriate null and alternative hypotheses. Ho: B₁ 0 H₂: B₁ = 0 O Ho: B₁ = 0 H₂: B₁ <0 ⒸH₁: B₁ = 0 H₂: B₁ > 0 Predictor Constant rainfall ⒸH₁: B₁ = 0 H₂: B₁ * 0 t= P-value= Stdev 2.349 0.03618 t-ratio -0.41 22.77 R-sq (adj) 97.4% = Compute the test statistic value and find the P-value. (Round your test statistic to two decimal places and your P-value to three P 0.686 0.000 State the conclusion in the problem context. (Use a = 0.05.) O Reject Ho. There is a useful linear relationship between runoff and rainfall at the 0.05 level. Reject Ho. There is not a useful linear relationship between runoff and rainfall at the 0.05 level. Fail to reject Ho. There is not a useful linear relationship between runoff and rainfall at the 0.05 level.
Consider the following data on x = rainfall volume (m³) and y = runoff volume (m³) for a particular location. X 4 12 14 17 23 30 40 47 55 67 72 82 96 112 127 y 4 10 13 15 15 25 27 46 38 46 53 70 82 99 100 Use the accompanying Minitab output to decide whether there is a useful linear relationship between rainfall and runoff. The regression equation is runoff = -0.97 +0.824 rainfall Coef -0.971 0.82401 s = 5.211 R-sq = 97.6% State the appropriate null and alternative hypotheses. Ho: B₁ 0 H₂: B₁ = 0 O Ho: B₁ = 0 H₂: B₁ <0 ⒸH₁: B₁ = 0 H₂: B₁ > 0 Predictor Constant rainfall ⒸH₁: B₁ = 0 H₂: B₁ * 0 t= P-value= Stdev 2.349 0.03618 t-ratio -0.41 22.77 R-sq (adj) 97.4% = Compute the test statistic value and find the P-value. (Round your test statistic to two decimal places and your P-value to three P 0.686 0.000 State the conclusion in the problem context. (Use a = 0.05.) O Reject Ho. There is a useful linear relationship between runoff and rainfall at the 0.05 level. Reject Ho. There is not a useful linear relationship between runoff and rainfall at the 0.05 level. Fail to reject Ho. There is not a useful linear relationship between runoff and rainfall at the 0.05 level.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter1: Functions
Section1.EA: Extended Application Using Extrapolation To Predict Life Expectancy
Problem 5EA
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Transcribed Image Text:Consider the following data on x = rainfall volume (m³) and y = runoff volume (m³) for a particular location.
X 4 12 14 17 23 30 40 47 55 67 72 82 96 112 127
y 4
10 13 15 15 25 27 46 38 46 53 70 82 99 100
Use the accompanying Minitab output to decide whether there is a useful linear relationship between rainfall and runoff.
O Ho: B₁ = 0
H₂: B₁ <0
The regression equation is
runoff
-0.97
Ho: B₁ = 0
H₂: B₁ > 0
Predictor
Constant
rainfall
State the appropriate null and alternative hypotheses.
OHO: B₁ #0
H₂: B₁ = 0
ⒸH₁: B = 0
Ha: ₁0
P-value=
+ 0.824 rainfall
Coef
-0.971
0.82401
Stdev
2.349
0.03618
s = 5.211 R-sq 97.6% R-sq (adj) 97.4%
t-ratio
Р
-0.41 0.686
22.77 0.000
Compute the test statistic value and find the P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.)
t=
State the conclusion in the problem context. (Use a = 0.05.)
O Reject Ho. There is a useful linear relationship between runoff and rainfall at the 0.05 level.
O Reject Ho. There is not a useful linear relationship between runoff and rainfall at the 0.05 level.
O Fail to reject Ho. There is not a useful linear relationship between runoff and rainfall at the 0.05 level.
Transcribed Image Text:Calculate a 95% confidence interval for the true average change in runoff volume associated with a 1 m³ increase in rainfall volume. (Round your answers to three decimal places.)
You may need to use the appropriate table in the Appendix of Tables to answer this question.
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