Question

trails in an experiment with a polygraph include 98 results that include 22 cases of wrong results and 79 cases of correct results. use a 0.01 significant 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 all 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.

Answer 1

Given : n=79

Let , X be the correct results and X=79

The estimate of the sample proportion is ,

The null and alternative hypothesis is ,

The test is left tailed test.

The test statistic is ,

Teh p-value is ,

p-value=

; From standard normal distribution table

Decision : Here , p-value =0.4404>0.01

Therefore , fail to reject the null hypothesis.

Conclusion : There is not sufficient evidence to support the claim that the polygraph results are correct less than 80% of the time.