Consider the following data on x = rainfall volume (m) and y = runoff volume (m) for a particular location. 12 14 17 23 30 40 49 55 67 72 83 96 112 127 4 10 13 15 15 25 27 46 38 46 53 70 82 99 103 Use the accompanying Minitab output to decide whether there is a useful linear relationship between rainfall and runoff. The regression equation is runoff = -2.00 + 0.841 rainfall Predictor Coef stdev t-ratio Constant -2.000 2.194 -0.91 0.379 rainfall 0.84079 0.03369 24.96 0.000 S = 4.823 R-sg = 98.04 R-sq (adj) = 97.8% State the appropriate null and alternative hypotheses. O Họ: B = 0 Hgi Bq 0 O Ho: Bq # 0 Hgi Bq = 0 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.) p-value = State the conclusion in the problem context. (Use a = 0.05.) O Reject H. There is a useful linear relationship between runoff and rainfall at the 0.05 level. O Reject H.. There is not a useful linear relationship between runoff and rainfall at the 0.05 level. O Fail to reject H. There is not a useful linear relationship between runoff and rainfall at the 0.05 level. O Fail to reject H. 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
Consider the following data on x = rainfall volume (m) and y = runoff volume (m) for a particular location. 12 14 17 23 30 40 49 55 67 72 83 96 112 127 4 10 13 15 15 25 27 46 38 46 53 70 82 99 103 Use the accompanying Minitab output to decide whether there is a useful linear relationship between rainfall and runoff. The regression equation is runoff = -2.00 + 0.841 rainfall Predictor Coef stdev t-ratio Constant -2.000 2.194 -0.91 0.379 rainfall 0.84079 0.03369 24.96 0.000 S = 4.823 R-sg = 98.04 R-sq (adj) = 97.8% State the appropriate null and alternative hypotheses. O Họ: B = 0 Hgi Bq 0 O Ho: Bq # 0 Hgi Bq = 0 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.) p-value = State the conclusion in the problem context. (Use a = 0.05.) O Reject H. There is a useful linear relationship between runoff and rainfall at the 0.05 level. O Reject H.. There is not a useful linear relationship between runoff and rainfall at the 0.05 level. O Fail to reject H. There is not a useful linear relationship between runoff and rainfall at the 0.05 level. O Fail to reject H. 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
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter1: Equations And Graphs
Section: Chapter Questions
Problem 10T: Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s...
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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.
7 12 14
17 23 30 40 49 55 67 72 83 96 112 127
4
10 13 15 15 25 27 46 38 46 53 70 82
99
103
Use the accompanying Minitab output to decide whether there is a useful linear relationship between rainfall and runoff.
The regression equation is
runoff = -2.00 + 0.841 rainfall
Predictor
Coef
Stdev
t-ratio
Constant
-2.000
2.194
-0.91
0.379
rainfall
0.84079
0.03369
24.96
0.000
s = 4.823
R-sg = 98.0%
R-sq (adj) = 97.8%
State the appropriate null and alternative hypotheses.
O Ho: B1 = 0
H: B, < 0
O Ho: B1 = 0
H: B, 0
O Ho: B1 = 0
H3: B, > 0
O Hoi Bq # 0
H: B1 = 0
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 =
P-value =
State the conclusion in the problem context. (Use a = 0.05.)
O Reject H.. There is a useful linear relationship between runoff and rainfall at the 0.05 level.
O Reject H.. There is not a useful linear relationship between runoff and rainfall at the 0.05 level.
O Fail to reject H.. There is not a useful linear relationship between runoff and rainfall at the 0.05 level.
O Fail to reject H.. 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.)
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