Respuesta :
Answer:
Given : Men challenged 1441 referee calls, with the result that 423 of the calls were overturned.
Women challenged 762 referee calls, and 210 of the calls were overturned.
To Find : Use a 0.01 significance level to test the claim that men and women have equal success in challenging calls. Test the claim using a hypothesis test.
Solution:
Men challenged 1441 referee calls, with the result that 423 of the calls were overturned.
[tex]n_1=1441\\y_1=423[/tex]
Women challenged 762 referee calls, and 210 of the calls were overturned.
[tex]n_2=762 \\y_2=210[/tex]
Let[tex]p_1[/tex]and[tex]p_2[/tex]be the probabilities of success of men and women receptively
[tex]H_0:p_1=p_2\\H_a:p_1\neq p_2[/tex]
We will use Comparing Two Proportions
[tex]\widehat{p_1}=\frac{y_1}{n_1}\\\widehat{p_1}=\frac{423}{1441}\\\widehat{p_1}=0.293\\\widehat{p_2}=\frac{y_2}{n_2}\\\widehat{p_2}=\frac{210}{762}\\\widehat{p_2}=0.2755[/tex]
[tex]\widehat{p}=\frac{y_1+y_2}{n_1+n_2} =\frac{423+210}{1441+762}=0.2873[/tex]
Formula of test statistic : [tex]\frac{\widehat{p_1}-\widehat{p_2}}{\sqrt{\widehat{p}(1-\widehat{p})(\frac{1}{n_1}+\frac{1}{n_2})}}[/tex]
Substitute the values
test statistic :[tex]\frac{0.293-0.2755}{\sqrt{0.2873(1-0.2873)(\frac{1}{1441}+\frac{1}{762})}}[/tex]
Test statistic : 0.863
Now refer the z table for p value
So. p = 0.8051
significance level = 0.01
p value > α
So, we accept the null hypothesis
So, men and women have equal success in challenging calls.
The Null and alternative hypotheses for the hypothesis test are respectively; p₁ = p₂ and p₁ ≠ p₂
What is the null and alternative hypothesis?
From the question, the claim is that men and women have equal success in challenging calls. This means that the proportion of men who challenge calls and get them overturned is the same as for the women. Both proportions are equal and thus, the null hypothesis here would be; p₁ = p₂
The alternative hypothesis is basically the opposite of the null hypothesis and as such our alternative hypothesis will be;
p₁ ≠ p₂
Read more about Null and Alternative Hypothesis at; https://brainly.com/question/13045159
