91影视

Out of 98 polygraph results, 74 are correct results, and 24 are wrong results.

The null hypothesis is written as follows.

The proportion of correct results is equal to 80%.

$H_0:p=0.80$

The alternative hypothesis is written as follows.

The proportion of correct results is less than 80%.

$H_1:p<0.80$

The test is left-tailed.

The sample size is n=98.

The sample proportion of correct results is computed below.

$$\begin{gathered} \hat{p}=\frac{\text{Number}\text{of}\text{correct}\text{results}}{\text{Sample}\text{Size}} \\ =\frac{74}{98} \\ =0.755 \end{gathered}$$

The population proportion of correct results is equal to 0.80.

The value of the test statistic is computed below.

$$\begin{gathered} z=\frac{\hat{p}-p}{\sqrt{\frac{pq}{n}}} \\ =\frac{0.755-0.80}{\sqrt{\frac{0.80\left(1-0.80\right)}{98}}} \\ =-1.111 \end{gathered}$$

Thus, z=-1.111.

Referring to the standard normal table, the critical value of z at $伪=0.05$ for a left-tailed test is equal to -1.645.

Referring to the standard normal table, the p-value for the test statistic value of -1.111 is equal to 0.1332.

As the p-value is greater than 0.05, the null hypothesis is failed to reject.

There is not enough evidence to support the claim that the proportion of correct results is less than 80%.

The sample proportion of correct polygraph results equal to 75.5% is not very high. Thus, polygraph results do not appear to have a high accuracy rate that is required to produce them in court.

Thus, their use in the court as evidence should be ceased.