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.

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 )
the test statistic is ( z=square ). (round to two decimal places as needed.)

Explanation:

Step1: Calculate the sample proportion

The sample proportion $\hat{p}=\frac{x}{n}$, where $x = 75$ (correct results) and $n=98$. So, $\hat{p}=\frac{75}{98}\approx0.7653$.

Step2: Calculate the test - statistic

The formula for the test - statistic in a one - sample proportion test is $z=\frac{\hat{p}-p}{\sqrt{\frac{p(1 - p)}{n}}}$. Here, $p = 0.80$ (from the null hypothesis $H_0:p = 0.80$), $n = 98$, and $\hat{p}\approx0.7653$.

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Answer:

The test statistic $z\approx - 0.86$