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). the test statistic in a two - tailed test is ( z = 1.95 ). o a. 0.0256; reject the null hypothesis o b. 0.0512; reject the null hypothesis o c. 0.0512; fail to reject the null hypothesis o d. 0.9744; fail to reject the null hypothesis

Explanation:

Step1: Find the P - value for a two - tailed test

For a two - tailed \(z\) - test, the P - value is \(2\times(1 - P(Z<|z|))\). Given \(z = 1.95\), from the standard normal table \(P(Z < 1.95)=0.9744\).
So the P - value \(=2\times(1 - 0.9744)=2\times0.0256 = 0.0512\).

Step2: Compare P - value with significance level

The significance level \(\alpha=0.05\). Since \(P - value=0.0512>0.05=\alpha\).

Answer:

C. \(0.0512\); fail to reject the null hypothesis