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

With H_1: p < 3/5, the test statistic is z = –1.68.

A) 0.093; fail to reject the null hypothesis
B) 0.0465; fail to reject the null hypothesis
C) 0.0465; reject the null hypothesis
D) 0.9535; fail to reject the null hypothesis

Answer 1

To find the P-value for the test statistic z = -1.68 in a left-tailed test (since \( H_1: p < \frac{3}{5} \)), you would look up the value of z = -1.68 in the standard normal (Z) table or use a calculator.

1. Finding the P-value:

   • The z-table provides the area to the left of the z value. For z = -1.68, the area is approximately 0.0465. This area represents the P-value for the left-tailed test.

2. Interpreting the P-value:

   • Compare the P-value (0.0465) to the significance level (\(\alpha = 0.05\)).
   • Since the P-value (0.0465) is less than the significance level (0.05), we reject the null hypothesis.

Conclusion: The correct answer is C) 0.0465; reject the null hypothesis.