Trials in an experiment with a polygraph include 99 results that include 23 case

Question

Trials in an experiment with a polygraph include 99 results that include 23 cases of wrong results and 76 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. Identify the null and alternative hypotheses. Choose the correct answer below. A. H_0: p = 0.20 H_1: p > 0.20 B. H_0: p = 0.20 H_1: p notequalto 0.20 C. H_0: p = 0.80 H_1: p

Explanation / Answer

a) option C) is correct

Ho : p = 0.80

Ha: p < 0.8 as the claim is if results are correct less than 80 %

here n = 99 , X= 76 , alpha = 0.05 (left -sided test)

Z = (p^ -p)/sqrt(pq/n)

Test and CI for One Proportion

Method

Descriptive Statistics

Test

Z= -0.55

p-value = P(Z < -0.55) = 0.290

since p-value > alpha

we fail to reject the null , there is not sufficient evidence

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p: event proportion Normal approximation method is used for this analysis.

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