12.27 Sleep Deprivation III Refer to the sleep deprivation experiment described in Exercise 12.11 and data set EX1211. The data and the MINITAB and Excel printouts are reproduced here.

a. Do the data present sufficient evidence to indicate that the number of errors is linearly related to the number of hours without sleep? Identify the two test statistics in the printout that can be used to answer this question.

b. Would you expect the relationship between y and x to be linear if x varied over a wider range (say, x = 4 to x = 48)?

c. How do you describe the strength of the relationship between y and x?

d. What is the best estimate of the common population variance o?

e. Find a 95% confidence interval for the slope of the line.

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Number of errors, y Number of hours without sleep, x Number of errors, y 8,6 6,10 8,14 8 12 16 14,12 16, 12 Number of hours without sleep, x 20 MINITAB ANOVA table for Exercise 12.27 Regression Analysis: y versus x The regression equation is y 3.00 +0.475 x 24 Predictor Coef SE Coef T P Constant 3.000 2.127 1.41 0.196 x 0.4750 0.1253 3.79 0.005 S = 2.24165 R-Sq 64.2% R-Sq(adj) 59.88 Analysis of Variance Source DF SS MS F P Regression 1 72.200 72.200 14.37 0.005 Residual Error 8 40.200 5.025 Total 9 112.400 Excel output for Exercise 12.27 ANOVA df SS MS F Significance F Regression 1 72.2 72.2 14.368 0.005 Residual 8 40.2 5.025 Total 9 112.4 Standard Lower Upper 95% Coefficients Error t Stat P-value 95% Intercept 3 x 0.475 2.1266 1.4107 0.1960 -1.9040 7.9040 0.1253 3.7905 0.0053 0.1860 0.7640