Question

Trials in an experiment with a polygraph include results that include cases of wrong results and cases of correct results. Use a significance level to test the claim that such polygraph results are correct less than ​% of the time. Identify the null​ hypothesis, alternative​ hypothesis, test​ statistic, P-value, conclusion about the null​ hypothesis, and final conclusion that addresses the original claim. Use the​ P-value method. Use the normal distribution as an approximation of the binomial distribution.

Answer 1

Answer and Step-by-step explanation:

This is a complete question

Trials in an experiment with a polygraph include 97 results that include 23 cases of wrong results and 74 cases of correct results. Use a 0.01 significance level to test the claim that such polygraph results are correct less than 80​% of the time. Identify the null​hypothesis, alternative​ hypothesis, test​ statistic, P-value, conclusion about the null​ hypothesis, and final conclusion that addresses the original claim. Use the​ P-value method. Use the normal distribution as an approximation of the binomial distribution.

The computation is shown below:

The null and alternative hypothesis is

$H_0 : p = 0.80$

$Ha : p < 0.80$

$\hat p = \frac{x}{ n} \\\\= \frac{74}{97}$

= 0.7629

Now Test statistic = z

$= \hat p - P0 / [\sqrtP0 \times (1 - P0 ) / n]$

$= 0.7629 - 0.80 / [\sqrt(0.80 \times 0.20) / 97]$

= -0.91

Now

P-value = 0.1804

$\alpha = 0.01$

$P-value > \alpha$

So, it is Fail to reject the null hypothesis.

There is ample evidence to demonstrate that less than 80 percent of the time reports that these polygraph findings are accurate.