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 left - tailed test is ( z=-2.05 ).
a. 0.0404; reject the null hypothesis
b. 0.4798; fail to reject the null hypothesis
c. 0.0202; reject the null hypothesis
d. 0.0453; fail to reject the null hypothesis

Explanation:

Step1: Find P - value for left - tailed test

For a left - tailed test with \(z=-2.05\), we use the standard normal distribution table. The P - value is \(P(Z < - 2.05)\).
Looking up \(z = 2.05\) in the standard normal table, \(P(Z<2.05)=0.9798\). Then \(P(Z < - 2.05)=1 - P(Z < 2.05)=1 - 0.9798 = 0.0202\)

Step2: Compare P - value with significance level

We are given a significance level \(\alpha=0.05\).
Since \(P - value=0.0202<\alpha = 0.05\), we reject the null hypothesis.

Answer:

C. 0.0202; reject the null hypothesis