Question

Since an instant replay system for tennis was introduced at a majorâ tournament, men challenged 1399 refereeâ calls, with the result that 411 of the calls were overturned. Women challenged 759 refereeâ calls, and 211of the calls were overturned.

Use a 0.01 significance level to test the claim that men and women have equal success in challenging calls.H0:p1=p2H1:p1 (does not equal) p2Identify the test statistic z=___

Answer 1

Answer: The value of test statistic is 0.696.

Explanation:

Since we have given that

`n_1=1399\\\\x_1=411\\\\p_1=(x_1)/(n_1)=(411)/(1399)=0.294`

Similarly,

`n_2=759, x_2=211\\\\p_2=(x_2)/(n_2)=(211)/(759)=0.278`

At 0.01 level of significance.

Hypothesis are :

`H_0:P_1=P_2=0.5\\\\H_a:P_1\\eq P_2`

So, the test statistic value would be

`z=\frac{(p_1-p_2)-(P_1-P_2)}{\sqrt{(P_1Q_1)/(n_1)+(P_2Q_2)/(n_2)}}\\\\z=\frac{0.294-0.278}{\sqrt{0.5* 0.5((1)/(1399)+(1)/(759))}}\\\\z=(0.016)/(0.023)=0.696`

Hence, the value of test statistic is 0.696.