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.