The standard deviation of math test scores at the one high school is 16.1. A teacher claims that standard deviation of girls' test scores is different from 16.1. A random sample of 22 girls results in scores with the standard deviation of 15.4.
a) Employ a significance level of 0.01 to test the teacher's claim.
b) Develop a 99% confidence interval for the true standard deviation of the girls' test scores.