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. Identity 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. Identity the null and alternative hypotheses. Choose the correct answer below. A. H_0: p = 0.80 H_1: = notequalto 0.80 B. H_0: p = 0.20 H_1: p notequalto 0.20 C. H_0: p = 0.20 H_1: p 0.80 E. H_0: p = 0.20 H_1: p > 0.20 F. H_0: p = 0.80 H_1: p

Explanation / Answer

The statistical software output for this problem is:

One sample proportion summary hypothesis test:
p : Proportion of successes
H0 : p = 0.8
HA : p < 0.8

Hypothesis test results:

Hence,

z = -0.55

p - Value = 0.2902

Fail to reject Ho

There is not sufficient evidence to conclude that results are correct less than 80% of the times.

Proportion Count Total Sample Prop. Std. Err. Z-Stat P-value p 77 99 0.77777778 0.040201513 -0.5527708 0.2902

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