With reference to Exercise 32, construct a 90% confidence interval for the standard deviation of the population sampled, that is, for the percentage of impurities in the given brand of peanut butter.
Exercise 32
A food inspector, examining 12 jars of a certain brand of peanut butter, obtained the following percentages of impurities: 2.3, 1.9, 2.1, 2.8, 2.3, 3.6, 1.4, 1.8, 2.1, 3.2, 2.0, and 1.9. Based on the modification of Theorem 1 of Exercise 7, what can she assert with 95% confidence about the maximum error if she uses the mean of this sample as an estimate of the average percentage of impurities in this brand of peanut butter?
Exercise 7
Modify Theorem 1 so that it can be used to appraise the maximum error when σ2 is unknown. (Note that this method can be used only after the data have been obtained.)
Theorem 1
