To find the test statistic for the claim regarding the standard deviation of all precipitation amounts, we will use the Chi-Squared test for variance. The formula for the test statistic \( \chi^2 \) is:
\[ \chi^2 = \frac{(n - 1) s^2}{\sigma_0^2} \]
where:
- \( n \) = sample size,
- \( s \) = sample standard deviation,
- \( \sigma_0 \) = claimed population standard deviation.
From the problem, we have:
- \( n = 26 \),
- \( s = 0.18 \),
- \( \sigma_0 = 0.25 \).
Step 1: Calculate the sample variance
First, we calculate \( s^2 \):
\[ s^2 = (0.18)^2 = 0.0324 \]
Next, we calculate \( \sigma_0^2 \):
\[ \sigma_0^2 = (0.25)^2 = 0.0625 \]
Step 2: Plug the values into the Chi-Squared formula
Now we can calculate the test statistic \( \chi^2 \):
\[ \chi^2 = \frac{(26 - 1) \cdot 0.0324}{0.0625} = \frac{25 \cdot 0.0324}{0.0625} \]
Calculating this step by step:
- \( 25 \cdot 0.0324 = 0.81 \)
- \( \chi^2 = \frac{0.81}{0.0625} \)
Continuing with the calculation:
\[ \chi^2 = 12.96 \]
Conclusion
The calculated test statistic is \( \chi^2 = 12.96 \).
Thus, the correct answer is C) 12.960.