Question

An electronic system was recently installed during a sports match to allow for an instant replay, allowing players to challenge a call made by a referee. During a recent survey, players made 839 challenges, and 327 of those challenges were overturned based on the instant replay. The claim is that the proportion of challenges that are successful is greater than one-third. Find a test statistic of the proportion.
z = 3.70



z = 3.03



z = 2.44



z = 3.47

Answer 1

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,

$p=\dfrac{327}{839}=0.39$

The claim is that the proportion of challenges that are successful is greater than one-third. So, the hypothesized population proportion is,

$P=\dfrac{1}{3}=0.33$

The test statistic of the proportion is a z-score (z) given by,

$z=\dfrac{p-P}{\sqrt{\frac{P(1-P)}{n}}}$

Putting the values,

$z=\dfrac{0.39-0.33}{\sqrt{\frac{0.33(1-0.33)}{839}}}=\dfrac{0.06}{\sqrt{\frac{0.33(0.67)}{839}}}=3.69\approx 3.70$