Question

trials in an experiment with a polygraph include 96 results that include 24 cases of wrong results and 72 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.
○ a. ( h_0:p = 0.80 )
( h_1:plt0.80 )
○ c. ( h_0:p = 0.80 )
( h_1:p
eq0.80 )
○ e. ( h_0:p = 0.20 )
( h_1:pgt0.20 )
○ b. ( h_0:p = 0.20 )
( h_1:plt0.20 )
○ d. ( h_0:p = 0.20 )
( h_1:p
eq0.20 )
○ f. ( h_0:p = 0.80 )
( h_1:pgt0.80 )

Explanation:

Step1: Understand the claim

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

Step2: Formulate null and alternative hypotheses

The null hypothesis \(H_0\) is a statement of equality. We assume no difference from the hypothesized proportion. The hypothesized proportion for the claim related to 80% (or \(p = 0.80\)) is the value in the null hypothesis. The alternative hypothesis \(H_1\) is the claim we are testing. Since the claim is \(p<0.80\) (correct less than 80% of the time), we set up:
\(H_0:p = 0.80\)
\(H_1:p<0.80\)

Answer:

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