A paper describes a study to determine the effects of several keyboard characteristics on typing speed. One of the variables considered was the front-to-back surface angle of the keyboard. Output resulting from fitting the simple linear regression model with x = surface angle (degrees) and y typing speed (words per minute) is given below. Reading the output: The Regression Analysis contains the regression equation as a function of x, a column of predictors (Constant is the y-intercept, Surface Angle is the independent variable), Coef is the estimated regression coefficients utilized in the regression equation, SE Coef is the standard error of the Predictor, T is the t-test statistic of the Predictor, P is the p- value of the Predictor), S is the standard error of the estimated model, R-sq is the coefficient of determination. Regression Analysis: Typing Speed versus Surface Angle The regression equation is Typing Speed 60.0+ 0.0036 Surface Angle SE Coef 0.2466 0.03956 Predictor Constant Surface Angle S 0.511766 State the appropriate null and alternative hypothesis. OH: B=0 H₂: B<0 OH: B=0 H: B> 0 OH: B>0 H₂: μ< 0 Coef 60.0284 0.00356 R-Sq 0.2% R-Sq (adj) 0.0% (a) Suppose that the basic assumptions of the simple linear regression model are met. Carry out a hypothesis test using α = 0.05 to decide if there is a useful linear relationship between x and y. Perform the Model Utility Test. O Ho: B<0 H₂: ß> 0 OH: B=0 H: Bao P-value = T 243.45 0.09 P 0.000 0.931 Calculate the test statistic and P-value for this test. (Round your test statistic to two decimal places and your P-value to three decimal places.) t = State the conclusion in the problem context. Owe fail to reject Ho. We do not have convincing evidence of a useful linear relationship between typing speed and surface angle. Owe fail to reject Ho. We have convincing evidence of a useful linear relationship between typing speed and surface angle. O We reject H. We do not have convincing evidence of a useful linear relationship between typing speed and surface angle. O We reject Ho. We have convincing evidence of a useful linear relationship between typing speed and surface angle. b) Are the values of s and r² consistent with the conclusion from part (a)? Explain. No, r₂ and se show almost no linear relationship between the two variables. O No, r₂ and se show a strong linear relationship between the two variables. O Yes, r₂ and se show almost no linear relationship between the two variables. O It is impossible to determine if r2 and se are consistent with the conclusion from part (a). O Yes, r₂ and se show a strong linear relationship between the two variables.