With reference to Exercise 11.65,

(a) find a \(99 \%\) confidence interval for the mean battery backup at \(x=1.25\);

(b) find \(95 \%\) limits of prediction for the battery backup provided by a laptop charged for 1.25 hours.

Data From Exercise 11.65

11.65 The data below pertains to the number of hours a lap- top has been charged for and the number of hours of backup provided by the battery. (a) Use the first set of expressions on page 330, in- volving deviations from the mean, to fit a least squares line to the observations. (b) Use the equation of the least squares line to esti mate the mean battery backup time at x = 3. Charged for Battery backup (hours) (hours) 0.5 0.75 1.0 1.75 1.5 2.5 2.0 4.5 2.5 6.0