91影视

Out of 879 challenges made by single players, a total of 231 are overturned. It is claimed that less than of $\frac{1}{3}$challenges are successful.

The null hypothesis is written as follows.

The proportion of successful challenges is equal to $\frac{1}{3}$.

$H_0:p=0.333$

The alternative hypothesis is written as follows.

The proportion of successful challenges is less than $\frac{1}{3}$.

$H_1:p<0.333$

The test is left-tailed.

The sample size is equal to n=879.

The sample proportion of successful challenges is computed below.

$$\begin{gathered} \hat{p}=\frac{\text{Number}\text{of}\text{successful}\text{challenges}}{\text{Sample}\text{Size}} \\ =\frac{231}{879} \\ =0.263 \end{gathered}$$

The population proportion of successful challenges is equal to 0.333.

The value of the test statistic is computed below.

$$\begin{gathered} z=\frac{\hat{p}-p}{\sqrt{\frac{pq}{n}}} \\ =\frac{0.263-0.333}{\sqrt{\frac{0.333\left(1-0.333\right)}{879}}} \\ =-4.404 \end{gathered}$$

Thus, z=-4.404.

Referring to the standard normal table, the critical value of z at $伪=0.01$for a left-tailed test is equal to -2.3263.

Referring to the standard normal table, the p-value for the test statistic value of -4.404 is equal to 0.00003.

As the p-value is less than 0.01, the null hypothesis is rejected.

There is enough evidence to support the claim that the proportion of successful challenges is less than $\frac{\mathbf{1}}{\mathbf{3}}$.

About 26.3% of the challenges raised are overturned, which doesn鈥檛 seem to be a very high percentage. Thus, the ability of referees to make the correct decision is evident.