trials in an experiment with a polygraph include 99 results that include 22 case

Question

trials in an experiment with a polygraph include 99 results that include 22 cases of wrong results and 77 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.

h0: p= 0.80 h1: p= < 0.80 What is the test statistic?

Explanation / Answer

  Let P be the proportion of correct results of all polygraph results

H0: P 0.80
Ha: P < 0.80

Estimated p = 77 / 99 = 0.777
Variance of proportion = p*(1-p)/n
= 0.8(0.2)/99 =0.0016
S.D. of p is sqrt[0.0016] = 0.0402
z = ( 0.777 - 0.8 ) / 0.0402 = -0.5721

P-value = P( z < -0.5721) =1P ( Z < 0.5721 ) = 10.7157 = 0.2843

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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