Since an instant replay system for tennis was introduced at

Since an instant replay system for tennis was introduced at a major tournament, men challenged 1417referee calls, with the result that 415of the calls were overturned. Women challenged 764referee calls, and 223 of the calls were overturned. Use a 0.05 significance level to test the claim that men and women have equal success in challenging calls. Complete parts (a) through (c) below.

Solution

Null Hypothesis, There Is No Significance between them Ho: p1 = p2
Alternate, men and women does n\'t have equal success in challenging calls H1: p1 != p2
Test Statistic
Sample 1 : X1 =415, n1 =1417, P1= X1/n1=0.293
Sample 2 : X2 =223, n2 =764, P2= X2/n2=0.292
Finding a P^ value For Proportion P^=(X1 + X2 ) / (n1+n2)
P^=0.293
Q^ Value For Proportion= 1-P^=0.707
we use Test Statistic (Z) = (P1-P2)/(P^Q^(1/n1+1/n2))
Zo =(0.293-0.292)/Sqrt((0.293*0.707(1/1417+1/764))
Zo =0.048
| Zo | =0.048
Critical Value
The Value of |Z | at LOS 0.05% is 1.96
We got |Zo| =0.048 & | Z | =1.96
Make Decision
Hence Value of |Zo | < | Z | and Here we Do not Reject Ho
P-Value: Two Tailed ( double the one tail ) -Ha : ( P != 0.0484 ) = 0.9614
Hence Value of P0.05 < 0.9614,Here We Do not Reject Ho

We have enough evidence that men and women have equal success in challenging calls