Answer:
The test statistic of the proportion is 3.70
Step-by-step explanation:
During a recent survey, players made 839 challenges, and 327 of those challenges were overturned based on the instant replay.
So the sample proportion is,
[tex]p=\dfrac{327}{839}=0.39[/tex]
The claim is that the proportion of challenges that are successful is greater than one-third. So, the hypothesized population proportion is,
[tex]P=\dfrac{1}{3}=0.33[/tex]
The test statistic of the proportion is a z-score (z) given by,
[tex]z=\dfrac{p-P}{\sqrt{\frac{P(1-P)}{n}}}[/tex]
Putting the values,
[tex]z=\dfrac{0.39-0.33}{\sqrt{\frac{0.33(1-0.33)}{839}}}=\dfrac{0.06}{\sqrt{\frac{0.33(0.67)}{839}}}=3.69\approx 3.70[/tex]
