We'll be using the $x^{2}$ cdf program again to find a p-value give a test statistic and a sample size, $\mathbf{n}$.

Follow the directions for a right tailed test for this problem provided on the handout. The bounds you need to enter in your calculator for a right tailed test are specified on the handout. Do not guess. Read and follow the directions.

Use Technology to find the p-value for the claim H1: $\sigma> 44.1$, if the test statistic is known to be $X^{2}=102.31$ and $n=71$.

Will the test statistic, $X^{2}=102.31$, be the upper or lower bound for a right tail test?
A. Upper bound, since we want the area to the left of this value for a right tail.
B. Lower bound, since we want the area to the right of this value for a right tail.

What is the p-value? $\square$ Round your answer to 4 decimal places.

Step 1 ：We are given the test statistic \(X^{2}=102.31\) and the sample size \(n=71\). We are asked to find the p-value for the claim \(H1: \sigma>44.1\).

Step 2 ：For a right tailed test, the test statistic will be the lower bound since we want the area to the right of this value.

Step 3 ：We use the chi-square cumulative distribution function (cdf) to find the p-value. The degrees of freedom is \(n-1=70\).

Step 4 ：We calculate the p-value as \(1 - \text{cdf}(X^{2}, df)\), where cdf is the cumulative distribution function of the chi-square distribution, \(X^{2}\) is the test statistic and \(df\) is the degrees of freedom.

Step 5 ：Substituting the given values, we get \(p-value = 1 - \text{cdf}(102.31, 70)\).

Step 6 ：The calculated p-value is approximately 0.0071.

Step 7 ：So, the test statistic, \(X^{2}=102.31\), will be the lower bound for a right tail test. The p-value is approximately \(\boxed{0.0071}\).