9. A tracking device, used for enabling robots to home in on a beacon that produces an audio signal, is said to be fine-tuned if the probability of correct identification of the direction of the beacon is the same for each side (left and right) of the tracking device. Out of 100 signals from the right, the device identifies the direction correctly 85 times. Out of 100 signals from the left, the device identifies the direction correctly 87 times.

(a) State the null and alternative hypotheses, carry out the test at level 0.01, and report the p-value.

(b) Construct a 99% CI for p1 − p2.

(c) Repeat parts

(a) and

(b) using R commands.