A manufacturer has been purchasing raw materials from a supplier whose consignments have a variance of 15.4 (in squared pounds) in impurity levels. A rival supplier claims that she can supply consignments of this raw material with the same mean impurity level but with lower variance. For a random sample of 25 consignments from the second supplier, the variance in impurity levels was found to be 12.2. What is the probability of observing a value this low or lower for the sample variance if, in fact, the true population variance is 15.4? Assume that the population distribution is normal.
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