Question

trials in an experiment with a polygraph include 98 results that include 22 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
oa ( h_{0}:p = 0.80 )
( h_{1}:p>0.80 )
ob. ( h_{0}:p = 0.20 )
( h_{1}:p<0.20 )
oc. ( h_{0}:p = 0.80 )
( h_{1}:p<0.80 )
od. ( h_{0}:p = 0.80 )
( h_{1}:p
eq0.80 )
oe ( h_{0}:p = 0.20 )
( h_{1}:p>0.20 )
of. ( h_{0}:p = 0.20 )
( h_{1}:p
eq0.20 )

Explanation:

Step1: Identify the claim

The claim is that polygraph results are correct less than 80% of the time. So, the population proportion \(p\) (correct results) is the parameter of interest.

Step2: Set up null and alternative hypotheses

The null hypothesis \(H_0\) is a statement of equality. The alternative hypothesis \(H_1\) is the claim we are testing.
Since the claim is \(p < 0.80\), the null hypothesis \(H_0:p = 0.80\) (assuming no difference from the - hypothesized 80% correct rate) and the alternative hypothesis \(H_1:p<0.80\)

Answer:

C. \(H_0:p = 0.80\), \(H_1:p < 0.80\)