Question

trials in an experiment with a polygraph include 98 results that include 23 cases of wrong results and 75 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. 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 = 0.80 )
( h_1: p>0.80 )
○ b. ( h_0: p = 0.80 )
( h_1: p<0.80 )
○ c. ( h_0: p = 0.80 )
( h_1: p
eq0.80 )
○ d. ( h_0: p = 0.20 )
( h_1: p>0.20 )
○ e. ( h_0: p = 0.20 )
( h_1: p<0.20 )
○ f. ( h_0: p = 0.20 )
( h_1: p
eq0.20 )

Explanation:

Step1: Determine the null and alternative hypotheses

The claim is that polygraph results are correct less than \(80\%\) of the time. So the null hypothesis \(H_0\) is the statement of equality, \(H_0:p = 0.80\). The alternative hypothesis \(H_1\) is the claim we are testing, \(H_1:p<0.80\)

Answer:

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