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 )

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 of success (\(p_1\) for men, \(p_2\) for women) are equal, i.e., \(H_0: p_1 = p_2\). The alternative hypothesis (\(H_1\)) for a two - tailed test (since we are testing for equality, the opposite is not equal) would be \(H_1: p_1
eq p_2\)? Wait, no, wait. Wait, the claim is equal success, so if we are testing the claim, the null is the claim, and the alternative is the opposite. Wait, but let's re - read. The claim is "men and women have equal success in challenging calls". So \(H_0: p_1 = p_2\), and \(H_1: p_1
eq p_2\)? But wait, looking at the options, option D: \(H_0:p_1 = p_2\), \(H_1:p_1
eq p_2\)? Wait, no, the options: Let's check the options again. Option D: \(H_0:p_1 = p_2\), \(H_1:p_1
eq p_2\)? Wait, the original problem's options:

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

Wait, but the claim is that they are equal, so the null hypothesis is the claim, \(H_0:p_1 = p_2\), and the alternative is that they are not equal, \(H_1:p_1
eq p_2\), which is option D? Wait, no, wait the options as per the image:

Wait the options:

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

The claim is that men and women have equal success, so the null hypothesis \(H_0\) is \(p_1 = p_2\) (the claim), and the alternative hypothesis \(H_1\) is the opposite of the claim, which is \(p_1
eq p_2\) (since we are testing if they are equal, the alternative is that they are not equal). So the correct option is D. \(H_0:p_1 = p_2\), \(H_1:p_1
eq p_2\)

Answer:

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