To find the P-value for this left-tailed chi-square hypothesis test, we can follow these steps:

1. Determine Degrees of Freedom: The degrees of freedom for this chi-square distribution is given as $df = 51$.
2. Given Chi-Square Value: The test statistic provided is $\chi^2_{51} = 35.548$.
3. Left-Tailed Test: Since this is a left-tailed test, we are interested in the probability $P(\chi^2 \leq 35.548)$ for a chi-square distribution with 51 degrees of freedom.

Using a chi-square distribution table or calculator, we can find the cumulative probability up to the test statistic value for a chi-square distribution with 51 degrees of freedom.

The approximate P-value for $\chi^2 = 35.548$ with $df = 51$ is:

$P \approx 0.9652$

Answer:

P-Value = 0.9652

Would you like a more detailed breakdown or have any questions?

Related Questions:

1. How is the P-value interpreted in hypothesis testing?
2. Why is it important to know if the test is one-tailed or two-tailed?
3. What changes in interpretation if the test were right-tailed instead of left-tailed?
4. How do degrees of freedom impact the shape of the chi-square distribution?
5. What conditions must be met to use a chi-square test?

Tip:

When performing a chi-square test, always verify if it's one-tailed or two-tailed, as this affects how you calculate the P-value.