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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.

The business college computing center wants to determine the proportion of business students who have personal computers (PCs) at home. If the proportion differs from 25%, then the lab will modify a proposed enlargement of its facilities. Suppose a hypothesis test is conducted and the test statistic is 2.4. Find the P-value for a two-tailed test of the hypothesis.

Learn how to calculate the P-value for a hypothesis test with a Z-score of 2.4. This detailed explanation covers hypothesis testing, normal distribution, and the use of a two-tailed test. Suitable for college-level statistics students.

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