Question

Since an instant replay system for tennis was introduced at a major​ tournament, men challenged 1430 referee​ calls, with the result that 426 of the calls were overturned. Women challenged

761 referee​ calls, and 210 of the calls were overturned. Use a 0.01 significance level to test the claim that men and women have equal success in challenging calls.

(1). Identify the test statistic. (2) P-Value  

Answer 1

To Test :-

H0 :- P1 = P2

H1 :- P1 P2

Test Statistic :-

is the pooled estimate of the proportion P
= ( x1 + x2) / ( n1 + n2)
= ( 426 + 210 ) / ( 1430 + 761 )
= 0.2903

Z = 1.0753

Test Criteria :-
Reject null hypothesis if

= 1.0753 < 2.5758, hence we fail to reject the null hypothesis
Conclusion :- We Fail to Reject H0

Decision based on P value
P value = 2 * P ( Z < 1.0753 )
P value = 0.2822
Reject null hypothesis if P value <
Since P value = 0.2822 > 0.01, hence we fail to reject the null hypothesis
Conclusion :- We Fail to Reject H0

There is sufficient evidence to support the claim that men and women have equal success in challenging calls.