Trials in an experiment with a polygraph include 97 results that include 23 cases of wrong results and 74 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.
Solution:
n = 97
x = 74
1 - x = 23
= x/n = 74/97 = 0.7629
Claim: p < 80% i.e. p < 0.80
The null and alternative hypothesis are
H0 : p = 0.80
H1 : p < 0.80
The test statistic z is
z =
= (0.7629 - 0.80)/[0.80*(1 - 0.80)/97]
= -0.91
Test statistic z = -0.91
For left tailed test :
p value = P(Z < z)
= P(Z < -0.91)
= 0.1814 (use z table)
p value = 0.1814
Use a 0.01 significance level .
p value is greater than 0.01
Decision : Fail to reject the null hypothesis,
Conclusion: Not sufficient evidence to support the claim that p is less than 80%
Trials in an experiment with a polygraph include 97 results that include 23 cases of wrong...
Trials in an experiment with a polygraph include 97 97 results that include 23 23 cases of wrong results and 74 74 cases of correct results. Use a 0.01 0.01 significance level to test the claim that such polygraph results are correct less than 80 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...
Trials in an experiment with a polygraph include 97 results that include 22 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...
Trials in an experiment with a polygraph include 98 results that include 24 cases of wrong results and 74 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 nuill hypothesis, and final conclusion that addresses the original claim. Use the P-value method. Use the normal distribution as an approximation of the binomial...
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