Question

Test the hypothesis using the P-value approach. Be sure to verify the requirments of the test.

Ho:p=0.6 versus H1:p>0.6

N= 100, x= 70, a= 0.05

Use technology to find the​ P-value.

​P-valueequals=

Answer 1

here n*p = 100 * 0.6 = 60 and n(1-p) = 100*0.4 = 40. Since both are > 10, we can assume normality and use z scores to calculate the test statistic and find the probability.

$\hat{p}$ = 70/100 = 0.7

The Hypothesis:

H0: p = 0.6 : The proportion is equal to 0.6.

H1: p > 0.6 : The proportion is greater than 0.6.

This is a right tailed test.

The Test Statistic:

$Z = \frac{\hat{p}-p}{\sqrt{\frac{p(1-p)}{n}}} = \frac{0.7-0.6}{\sqrt{\frac{0.6*0.4}{100}}} = 2.04$

The p Value:    The p value (Right tail) for Z = 2.04, is; p value = 0.0207

The Decision Rule: If the P value is < $\alpha$, Then Reject H0

The Decision: Also since P value (0.0207) is < $\alpha$ (0.05), We Reject H0.

The Conclusion: There is sufficient evidence at the 95% significance level to conclude that the proportion is greater than 0.6.