1 A tracking device used for enabling robots to home in on a

1. A tracking device, used for enabling robots to home in on a beacon which produces an audio signal, is said to be fine-tuned if the probability of correct identification 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. Test whether the device is fine-tuned at = .01.

Please provide steps

Solution

Null, There Is No Significance between them Ho: p1 = p2
Alternate , There Is Significance between them H1: p1 != p2
Test Statistic
Sample 1 : X1 =85, n1 =100, P1= X1/n1=0.85
Sample 2 : X2 =87, n2 =100, P2= X2/n2=0.87
Finding a P^ value For Proportion P^=(X1 + X2 ) / (n1+n2)
P^=0.86
Q^ Value For Proportion= 1-P^=0.14
we use Test Statistic (Z) = (P1-P2)/(P^Q^(1/n1+1/n2))
Zo =(0.85-0.87)/Sqrt((0.86*0.14(1/100+1/100))
Zo =-0.408
| Zo | =0.408
Critical Value
The Value of |Z | at LOS 0.01% is 2.576
We got |Zo| =0.408 & | Z | =2.576
Make Decision
Hence Value of |Zo | < | Z | and Here we Do not Reject Ho
P-Value: Two Tailed ( double the one tail ) -Ha : ( P != -0.4076 ) = 0.6836
Hence Value of P0.01 < 0.6836,Here We Do not Reject Ho

probability of correct identification of the beacon is the same for each side
(left and right) of the tracking device