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 0.05 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. Identify the null and alternative hypotheses. Choose the correct answer below. The test statistic is z. (Round to two decimal places as needed.) The P-value is. (Round to four decimal places as needed.) Identify the conclusion about the null hypothesis and the final conclusion that addresses the original claim. H_0. There sufficient evidence to support the claim that the polygraph results are correct less than 80% of the time.

Explanation / Answer

a) here the null hypothesis = Ho = p = 0.8

the alternate hypothesis = Ha = P<0.8

hence option F is correct

b) p = 77/99 - 0.77

the z static = (0.77 - 0.80) /sqrt(0.80*0.20/(99))

= -0.75

c) the p value for z = -0.75 from z table = 0.2266

d) as the p value if greater then the significance level therefore we will reject the null hypothesis an there is sufficient evident

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