Question

since an instant replay system for tennis was introduced at a major tournament, men challenged 1394 referee calls, with the result that 417 of the calls were overturned. women challenged 779 referee calls, and 216 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.

a. test the claim using a hypothesis test.
consider the first sample to be the sample of male tennis players who challenged referee calls and the second sample to be the sample of female tennis players who challenged referee calls. what are the null and alternative hypotheses for the hypothesis test?
a. ( h_0: p_1 geq p_2 ) ( h_1: p_1
eq p_2 )
b. ( h_0: p_1 = p_2 ) ( h_1: p_1 > p_2 )
c. ( h_0: p_1
eq p_2 ) ( h_1: p_1 = p_2 )
d. ( h_0: p_1 = p_2 ) ( h_1: p_1
eq p_2 )
e. ( h_0: p_1 leq p_2 ) ( h_1: p_1
eq p_2 )
f. ( h_0: p_1 = p_2 ) ( h_1: p_1 < p_2 )

identify the test statistic.
( z = square ) (round to two decimal places as needed)

Explanation:

The claim is that men and women have equal success in challenging calls, so the null hypothesis \(H_0\) should state that the proportions \(p_1\) (men) and \(p_2\) (women) are equal (\(p_1 = p_2\)). The alternative hypothesis \(H_1\) for a two - tailed test (since we are testing for equality, any difference would be a two - tailed case) should state that \(p_1
eq p_2\). Looking at the options, option D has \(H_0:p_1 = p_2\) and \(H_1:p_1
eq p_2\) which matches our reasoning.

Answer:

D. \(H_0:p_1 = p_2\), \(H_1:p_1
eq p_2\)