14. Chemical Purity A chemical manufacturer claims that the purity of his product never varies by more than 2%. Five batches were tested and given purity readings of 98.2, 97.1, 98.9, 97.7, and 97.9%.

a. Do the data provide sufficient evidence to contradict the manufacturer’s claim? (hint: To be generous, let a range of 2% equal 4 .)

b. Find a 90% confidence interval for  2