Consider the following data on x = rainfall volume (m³) and y = runoff volume (m²) for a particular location. x 5 12 14 20 23 30 40 50 55 67 72 84 96 112 127 y 4 10 13 15 15 25 27 44 38 46 53 71 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 -1.95 ⒸHg: ₂0 H₂: ₂0 State the appropriate null and alternative hypotheses. ⒸH₂: B₂0 H₂: A₂=0 ⒸH₂: ₂0 H₂: A₂ > 0 ⒸHg: ₂0 H₂: A₂ <0 +0.832 rainfall Coef -1.952 0.83183 Predictor Stdev Constant 2.129 rainfall 0.03261 s - 4.671 R-sq- 98.0% R-sq (adj) 97.98 P-value= t-ratio -0.92 25.51 P 0.376 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.) State the conclusion in the problem context. (Use a = 0.05.) Reject Ho. There is a useful linear relationship between runoff and rainfall at the 0.05 level. O Reject Hg. 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. O Fail to reject Ho. There is a useful linear relationship between runoff and rainfall at the 0.05 level. 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.) 7) m²
Consider the following data on x = rainfall volume (m³) and y = runoff volume (m²) for a particular location. x 5 12 14 20 23 30 40 50 55 67 72 84 96 112 127 y 4 10 13 15 15 25 27 44 38 46 53 71 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 -1.95 ⒸHg: ₂0 H₂: ₂0 State the appropriate null and alternative hypotheses. ⒸH₂: B₂0 H₂: A₂=0 ⒸH₂: ₂0 H₂: A₂ > 0 ⒸHg: ₂0 H₂: A₂ <0 +0.832 rainfall Coef -1.952 0.83183 Predictor Stdev Constant 2.129 rainfall 0.03261 s - 4.671 R-sq- 98.0% R-sq (adj) 97.98 P-value= t-ratio -0.92 25.51 P 0.376 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.) State the conclusion in the problem context. (Use a = 0.05.) Reject Ho. There is a useful linear relationship between runoff and rainfall at the 0.05 level. O Reject Hg. 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. O Fail to reject Ho. There is a useful linear relationship between runoff and rainfall at the 0.05 level. 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.) 7) m²
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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 5 12 14 20 23 30 40 50 55 67 72 84 96 112 127
y 4 10 13 15 15 25 27 44 38 46 53 71 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 -1.95
Ho: P₁=0
H₂: A₂ #0
State the appropriate null and alternative hypotheses.
Ho: P₂ #0
H₂: A₁ = 0
Ho: B₂=0
H₂: A₂ > 0
ⒸH₂= P₂ = 0
Hg: A₂ <0
+ 0.832 rainfall
Coef
-1.952
0.83183 0.03261
s- 4.671 R-sq 98.08 R-sq (adj) - 97.98
Predictor
Constant
rainfall
P-value=
Stdev
2.129
t-ratio
-0.92
25.51
P
0.376
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.)
Ⓒ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.
O Fail to reject Ho. There is a useful linear relationship between runoff and rainfall at the 0.05 level.
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.)
m³
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