A motorist found that the efficiency of her engine could be increased by adding lubricating oil to fuel. She experimented with different amounts of lubricating oil and the data are

(a) Obtain the least squares fit of a straight line to the amount of lubricating oil.

(b) Test whether or not the slope \(\beta=0\). Take \(\alpha=\) 0.05 as your level of significance.

(c) Give a point estimate of the mean engine efficiency when the amount of lubricating oil is \(450 \mathrm{ml}\).

(d) What additional danger is there when using your estimate in part (c)?

(e) How would you randomize this experiment?

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Amount of lubricating oil (ml) Efficiency (%) 0 60 25 70 50 75 75 81 100 84