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 \(\boxed{0.0071}\).