The question asks for the P-value given a test statistic of 2.4 for a two-tailed test of a hypothesis, where the proportion differs from 25%. Here's how we calculate the P-value:

1. Determine the test statistic (Z): It's given as $Z = 2.4$.

2. Find the P-value for a two-tailed test:

   The P-value in a two-tailed test corresponds to the probability that the test statistic falls in the extreme tails of the normal distribution (both sides). We need to look up the value for $Z = 2.4$ in a Z-table or use statistical software.

   The area to the right of $Z = 2.4$ (one-tailed) is approximately 0.0082. Since it's a two-tailed test, we multiply this by 2:

   $\text{P-value} = 2 \times 0.0082 = 0.0164$

Thus, the correct answer is C. 0.0164.

Would you like further details or have any questions?

Here are five related questions you might find useful:

1. What is the significance level (α) in hypothesis testing?
2. How is a two-tailed test different from a one-tailed test?
3. What does a P-value represent in hypothesis testing?
4. How do you interpret a P-value in the context of statistical significance?
5. What is the relationship between Z-scores and confidence intervals?

Tip: A lower P-value indicates stronger evidence against the null hypothesis, suggesting that the observed data is less likely to occur under the assumption that the null hypothesis is true.