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Since an instant replay system for tennis was introduced at a major tournament, men challenged 1420 referee calls, with the result that 416 of the calls were overturned. Women challenged 739 referee calls, and 215 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. [tex]$H_0: p_1=p_2$[/tex]
[tex]$H_1: p_1 \neq p_2$[/tex]

B. [tex]$H_0: p_1=p_2$[/tex]
[tex]$H_1: p_1 \ \textgreater \ p_2$[/tex]

C. [tex]$H_0: p_1=p_2$[/tex]
[tex]$H_1: p_1 \neq p_2$[/tex]

D. [tex]$H_0: p_1 \leq p_2$[/tex]
[tex]$H_1: p_1 \ \textless \ p_2$[/tex]

E. [tex]$H_0: p_1 \geq p_2$[/tex]
[tex]$H_1: p_1 \neq p_2$[/tex]

F. [tex]$H_0: p_1=p_2$[/tex]
[tex]$H_1: p_1 \neq p_2$[/tex]



Answer :

GinnyAnswer
To test the claim that men and women have equal success in challenging calls, we start by stating the null and alternative hypotheses. The null hypothesis, [tex]\( H_0 \)[/tex], states that the population proportions of successful challenges for men and women are equal, while the alternative hypothesis, [tex]\( H_1 \)[/tex], states that the proportions are not equal.

The correct hypotheses are:
- Null hypothesis ([tex]\( H_0 \)[/tex]): [tex]\( p_1 = p_2 \)[/tex]
- Alternative hypothesis ([tex]\( H_1 \)[/tex]): [tex]\( p_1 \neq p_2 \)[/tex]

So, the correct choice is:

A. [tex]\( H_0: p_1 = p_2 \)[/tex]

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