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. 0.0901, reject the null hypothesis d. 0.9099, fail to reject the null hypothesis

Explanation:

Step1: Find the p - value

Since \(H_1:p > 0.554\) (right - tailed test), and \(z = 1.34\).
The p - value for a right - tailed test with test statistic \(z\) is \(P(Z>z)\).
We know that \(P(Z > 1.34)=1 - P(Z\leq1.34)\).
From the standard normal table, \(P(Z\leq1.34)=0.9099\).
So \(P(Z > 1.34)=1 - 0.9099 = 0.0901\).

Step2: Make a decision

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

Answer:

C. 0.0901, fail to reject the null hypothesis