Question

use the given information to find the p - value. also, use a 0.05 significance level and state the conclusion al 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. 0.1802; reject the null hypothesis b. 0.9099; fail to reject the null hypothesis c. 0.0901; fail to reject the null hypothesis d. 0.0901; reject the null hypothesis

Explanation:

Step1: Find the p - value

Since \(H_1:p > 0.554\), this is a right - tailed test.
For a standard normal distribution \(Z\), the p - value is \(P(Z>z)\). Given \(z = 1.34\).
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