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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.

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Kalahira
Answer: Let P be the proportion of correct results of all polygraph results 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 0.05, 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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