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).

Question

The test statistic in a left-tailed test is z = –2.05.

A) 0.4798; fail to reject the null hypothesis
B) 0.0404; reject the null hypothesis
C) 0.0453 fail to reject the null hypothesis
D) 0.0202; reject the null hypothesis

Answer 1

To find the P-value for the given test statistic \( z = -2.05 \) in a left-tailed test, we can look up the value in the standard normal (Z) distribution table, or we can use a calculator or statistical software.

A \( z \) value of \(-2.05\) indicates that we are looking for the area to the left of \(-2.05\) under the standard normal curve.

Using a Z-table or calculator, we find:

• The P-value corresponding to \( z = -2.05 \) is approximately \( 0.0202 \).

Now we compare the P-value with the significance level of \( \alpha = 0.05 \):

• Since \( 0.0202 < 0.05 \), we reject the null hypothesis.

Thus, the correct choice is:

D) 0.0202; reject the null hypothesis.