A group of 13 children and adolescents (considered healthy) participated in a psychological study designed to analyze the relationship between age and average total sleep time (ATST). To obtain a measure for ATST (in minutes), recordings were taken on each subject on three consecutive nights and then averaged. The results obtained are displayed in the following table.

a. Determine the least-squares estimates of the slope and intercept for the straight-line regression of ATST (Y) on AGE (X). Draw the estimated line on the accompanying scatter diagram, and comment on the fit.
b. Are any of the assumptions for straight-line regression clearly not satisfied in this example?
c. Test the null hypothesis that the true slope is 0; be sure to interpret your result.
d. Obtain a 95% confidence interval for β1. Interpret your result.
e. Would you reject the null hypothesis H0: β1 = 0 based on the confidence interval you calculated in part (d)? Explain.
f. Determine and sketch 95% confidence bands on the accompanying scatter diagram. Use your diagram to estimate the mean ATST when AGE = 10. Interpret your result.

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ATST ATST (min/24 h) AGE (min/24 h) AGE 586.00 4.40 461.75 14.00 49110 10.10 515.20 8.90 93.00 11.10 528.30 7.75 565.00 6.70 462.00 11.50 532.10 9.60 77.6012.40 575.90 5.50 532.50 8.60 530.50 7.20 700 600 550 450 5 15 AGE (X) (ys)