9.83 Two types of aluminum powders are blended before a sintering process is begun to form solid aluminum. The adequacy of the blending is gauged by taking numerous small samples from the blend and measuring the weight proportion of one type of powder. For adequate blending, the weight proportions from sample to sample should have small variability. Thus, the variance becomes a key measure of blending adequacy.

Ten samples from an aluminum blend gave the following weight proportions for one type of powder:
0.52, 0.54, 0.49, 0.53, 0.52, 0.56, 0.48, 0.50, 0.52, 0.51 a Estimate the population variance in a 95%
confidence interval.
b What assumptions are necessary for your answer in part

(a) to be valid? Are the assumptions reasonable for this case?