A food inspector, examining 12 jars of a certain brand of peanut butter, obtained from the fofollowing 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 11.1 of Exercise 11.7, 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? Theorem 11.1: If X(with the bar over it), the mean of a random sample of size n from a normal population with the known variance sigma squared, is to be used as an estimator of the mean of the population, the probability is 1-alpha that the error will be less than z alpha/2 times sigma/square root of n. Exercise 11.7: Modify Theorem 11.1 so that if can be used to appraise the maximum error when sigma squared is unknown. (Note that this method can be used only after the data have been obtained.)