Answer:
The answer is 2.0190
Step-by-step explanation:
From the given question,
We recall that,
p = 141/241 = 0.5850
so, p = 0.5
The Hypothesis is:
H₀ : P = 0.5, this means that H0:50% of the games played will be won
vs
H₁ : P > 0.5, This indicates that, win is greater than 0.5 due to home field advantages.
n=241,x=141
Then,
SD(p)=√(p*q/n)=√(0.5*0.5/141)=0.0421
z = p - p/ SD (p) = 0.5850 - 0.5/0.0421 = 0.085/0.0421 =2.0190
therefore, there is strong evidence that there is home field advantages in professional football.
Following are the calculation to the hypothesis test:
[tex]\to \hat{p}= \frac{141}{241}=0.5850 \\\\\to p=0.5[/tex]
Hypothesis:
[tex]H_{0}:P=0.5[/tex] implies [tex]H_0:50\%[/tex] of a games would be won.
vs
[tex]H_{1}:P>0.5[/tex] because of home-field advantages, the victory exceeds [tex]0.5[/tex] . [tex]\to n=241 \\\\\to x=141\\\\\to SD(p)=\sqrt{(\frac{p\times q}{n})}=\sqrt{(\frac{0.5\times 0.5}{241})}=\sqrt{(\frac{0.25}{241})}= \sqrt{0.001}=0.0322 \\\\\to z=\frac{\hat{p}-p}{SD(p))}=\frac{0.5850-0.5}{0.0322}=\frac{0.085}{0.0322}=1.624\\\\ \to P(Z>1.624)=0.0521879[/tex]
conclusion [tex]P-value =0.0521879<0.05[/tex], As a result, we reject the null hypothesis, i.e. there's really significant evidence that home-field advantage exists in pro football.
Learn more:
brainly.com/question/17854172
