Consider the following data on x rainfall volume m3 and y

Consider the following data on x = rainfall volume (m^3) and y = runoff volume (m^3) for a particular location. Use the accompanying Minitab output to decide whether there is a useful linear relationship between rainfall and runoff. The regression equation is runoff = -1.43 + 0.830 rainfall State the appropriate null and alternative hypotheses. 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 alpha = 0.05.) Reject H0. There is a useful linear relationship between runoff and rainfall at the 0.05 level. Reject H0. There is not a useful linear relationship between runoff and rainfall at the 0.05 level. Fail to reject H0. There is not a useful linear relationship between runoff and rainfall at the 0.05 level. Fail to reject H0. 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 m^3 increase in rainfall volume. (Round your answers to three decimal places.) m^3

Solution

t=24.07

P=0.000

95% CI=( b +- t*se)

95% CI=(0.83042-2.16*0.0345, 0.83042+2.16*0.0345)

=(0.7559, 0.90494)

95% CI = (0.756, 0.905)   ( WITH THREE DECIMALS)