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.

Step-by-step explanation:

Since we have given that

$n_1=1399\\\\x_1=411\\\\p_1=\dfrac{x_1}{n_1}=\dfrac{411}{1399}=0.294$

Similarly,

$n_2=759, x_2=211\\\\p_2=\dfrac{x_2}{n_2}=\dfrac{211}{759}=0.278$

At 0.01 level of significance.

Hypothesis are :

$H_0:P_1=P_2=0.5\\\\H_a:P_1\neq P_2$

So, the test statistic value would be

$z=\dfrac{(p_1-p_2)-(P_1-P_2)}{\sqrt{\dfrac{P_1Q_1}{n_1}+\dfrac{P_2Q_2}{n_2}}}\\\\z=\dfrac{0.294-0.278}{\sqrt{0.5\times 0.5(\dfrac{1}{1399}+\dfrac{1}{759})}}\\\\z=\dfrac{0.016}{0.023}=0.696$

Hence, the value of test statistic is 0.696.