Choose the correct​ P-value.

A.0.3504

0.35040.3504

B.0.0527

0.05270.0527

C.0.2152

0.21520.2152

D.0.0383

0.0383

To choose the correct p-value, we need to compare the calculated chi-squared test statistic to the chi-squared distribution table or use statistical software to find the corresponding p-value.

Given that the chi-squared test statistic we calculated is approximately \(4.294\), and we have 1 degree of freedom, we compare this against the chi-squared distribution.

Looking up the p-value for a chi-squared value of \(4.294\) with \(1\) degree of freedom:

- The p-value is the area under the chi-squared distribution curve to the right of our calculated \(\chi^2\) value.

Given the choices:

- **A. 0.3504**: This is too high; it would correspond to a much smaller chi-squared statistic.
- **B. 0.0527**: This is close to the significance level of \(0.05\), but slightly above it.
- **C. 0.2152**: This is also too high; it would correspond to a smaller chi-squared statistic.
- **D. 0.0383**: This is below \(0.05\) and corresponds to a \(\chi^2\) value slightly above 4.

Based on this information, the correct p-value corresponding to our calculated \(\chi^2\) statistic of \(4.294\) is **D. 0.0383**.

Would you like any further explanations or have any more questions?

Here are some follow-up questions for practice:

1. How do you interpret a p-value of 0.0383 in the context of hypothesis testing?
2. What would your conclusion be if the p-value was higher than 0.05?
3. Can you explain the relationship between the chi-squared statistic and the p-value?
4. How is the significance level related to the p-value?
5. What does it mean if the p-value is very close to the significance level (e.g., 0.049)?
6. How does the number of degrees of freedom affect the p-value in a chi-squared test?
7. Why might a researcher choose a different significance level (e.g., 0.01 or 0.10)?
8. What steps would you take if the p-value was inconclusive (e.g., exactly 0.05)?

**Tip**: Always ensure that your p-value interpretation aligns with the context of your hypothesis test, especially when deciding whether to reject or fail to reject the null hypothesis.

Learn how to choose the correct p-value in a chi-squared test with a detailed explanation. This problem involves statistical analysis using the chi-squared test statistic and distribution. Understand the significance level and statistical inference. Suitable for undergraduate students and researchers.

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