Question

Since an instant replay system for tennis was introduced at a major​ tournament, men challenged 1389 referee​ calls, with the result that 421 of the calls were overturned. Women challenged 761 referee​ calls, and 213 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. What is the conclusion of the hypothesis

Answer 1

We conclude that men and women have equal success in challenging calls.

Explanation:

We are given that an instant replay system for tennis was introduced at a major​ tournament, men challenged 1389 referee​ calls, with the result that 421 of the calls were overturned. Women challenged 761 referee​ calls, and 213 of the calls were overturned.

Let
`p_1` = proportion of calls overturned that were challenged by men

`p_2` = proportion of calls overturned that were challenged by women

So, Null Hypothesis,
`H_0` :
`p_1-p_2` = 0 or
`p_1=p_2` {means that men and women have equal success in challenging calls}

Alternate Hypothesis,
`H_A` :
`p_1-p_2\\eq 0` or
`p_1\\eq p_2` {means that men and women does not have equal success in challenging calls}

The test statistics that would be used here One-sample z proportion statistics;

T.S. =
`\frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{(\hat p_1(1-\hat p_1))/(n_1)+(\hat p_2(1-\hat p_2))/(n_2) } }` ~ N(0,1)

where,
`\hat p_1` = sample proportion of calls overturned by men =
`(421)/(1389)` = 0.30

`\hat p_2` = sample proportion of calls overturned by women =
`(213)/(761)` = 0.28

`n_1` = sample of referee calls challenged by men = 1389

`n_2` = sample of referee calls challenged by women = 761

So, test statistics =
`\frac{(0.30-0.28)-(0)}{\sqrt{(0.30(1-0.30))/(1389)+(0.28(1-0.28))/(761) } }`

= 0.98

The value of test statistics is 0.98.

Now, at 0.05 significance level the z table gives critical value of -1.96 and 1.96 for two-tailed test. Since our test statistics lies within the range of critical values of z, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.

Therefore, we conclude that men and women have equal success in challenging calls.