To solve this, we need to find the probability $P(X > 13.843)$ for a chi-squared distribution with 4 degrees of freedom.

1. Determine the distribution: $X \sim \chi^2(4)$, meaning $X$ has a chi-squared distribution with 4 degrees of freedom.

2. Locate the value on the chi-squared table or use a calculator: The probability $P(X > 13.843)$ corresponds to finding the area to the right of 13.843 in a chi-squared distribution with 4 degrees of freedom.

3. Use a calculator or table: For a chi-squared distribution with 4 degrees of freedom, the value of 13.843 typically corresponds to the upper tail probability around $\alpha = 0.01$.

Therefore: $P(X > 13.843) \approx 0.01$

The answer, rounded to two decimal places, is approximately 0.01.

Would you like more details or have any questions?

Related Questions

1. How do you find critical values in a chi-squared distribution?
2. What are common uses of chi-squared distributions in hypothesis testing?
3. How do you interpret a chi-squared statistic in goodness-of-fit tests?
4. How can you compute chi-squared probabilities without a calculator?
5. What are the properties of the chi-squared distribution?

Tip

Using statistical tables or software like Stat Trek can make finding chi-squared probabilities faster and more accurate.