Trials in an experiment with a polygraph include 98 results that include 24 case

Question

Trials in an experiment with a polygraph include 98 results that include 24 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.

Explanation / Answer

Solution:-

H0: P 0.80
Ha: P < 0.80

Estimated p = 74 / 98 = 0.7551
Variance of proportion = p*(1-p)/n
= 0.8(0.2)/98 =0.0016327
S.D. of p is sqrt[0.001633] = 0.0404
z = ( 0.7551 - 0.8 ) / 0.0404 = -1.1112

P-value = P( z < -1.1112) = 0.1335

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.

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