Trials in an experiment with a polygraph include 96 results that include 24 case

Question

Trials in an experiment with a polygraph include 96 results that include 24 cases of wrong results and 72 cases of correct results. Use a 0.05 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. Let p be the population proportion of correct polygraph results. ldentify the null and alternative hypotheses. Choose the correct answer below A. Ho: p 0.80 H1: p#0.80 ° C. Ho:p#0.80 H1: p> 0.80 OE. Ho:p=0.80 H1: p 0.20 OF. Ho:p=0.20 H1: p

Explanation / Answer

Solution:

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

E. H0: P = 0.80
H1: P < 0.80

Estimated p = 72 / 96 = 0.75
Variance of proportion = p*(1-p)/n
= 0.75(0.25)/96 = 0.0019
S.D. of p is sqrt[0.0019] = 0.0435
Test statistic z = ( 0.75- 0.80) / 0.0435 = -1.1494

P-value = P( z < -1.1494) = 0.1252

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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