Question

Trials in an experiment with a polygraph include 99 results that include 24 cases of wrong results and 75 cases of correct results. Use a 0.01 significance level to test the claim that such polygraph results are correct last then 80% of the time. identifying 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 and use the normal distribution as an approximation of the binomial

Answer 1

SOLUTION:

From given data,

Trials in an experiment with a polygraph include 99 results that include 24 cases of wrong results and 75 cases of correct results. Use a 0.01 significance level to test the claim that such polygraph results are correct last then 80% of the time.

To test the hypothesis is that the proportion of polygraph result are correct is less than 80% of time at 1% level of significance.

The null and alternative hypothesis is,

H₀: P = 0.80
H_a: P < 0.80

The value of test statistics is,

Where,

The point estimated of the proportion is given as:

p = 75 / 99 = 0.7575

z = -1.06
The value of test statistics is -1.06

The P-value for this test is,

From the standard normal distribution table , the associated probability for the area to the left is shown below

P-value = P( z < -1.06 ) = 0 .144572.

The P-value for this is 0.144572

Decision

Since the p-value is greater than 0.01, we do not reject the null hypothesis. Based on the results there is no evidence that polygraph test results should be prohibited as evidence in trials.