Question

use the given information to find the p - value. also, use a 0.05 significance level and state the conclusion about the null hypothesis (reject the null hypothesis or fail to reject the null hypothesis). with ( h_1:p>0.554 ), the test statistic is ( z = 1.34 ).

a. 0.0901; fail to reject the null hypothesis
b. 0.1802; reject the null hypothesis
c. 0.9099; fail to reject the null hypothesis
d. 0.0901; reject the null hypothesis

Explanation:

Step1: Find p - value for right - tailed test

For a right - tailed test with test statistic \(z = 1.34\), the p - value is \(P(Z>1.34)\).
Since \(P(Z > z)=1 - P(Z\leq z)\), and from the standard normal table \(P(Z\leq1.34)=0.9099\).
So \(P(Z > 1.34)=1 - 0.9099 = 0.0901\).

Step2: Compare p - value with significance level

The significance level \(\alpha=0.05\).
Since \(p - value=0.0901>0.05=\alpha\), we fail to reject the null hypothesis.

Answer:

A. 0.0901; fail to reject the null hypothesis