The variance of the SAT scores for all students who took that test this year is 5000. The variance of the SAT scores for a random sample of 20 students from one school is equal to 3175.
a. Test at a 2.5% significance level whether the variance of the SAT scores for students from this school is lowers than 5000. Assume that the SAT scores for all students at this school are (approximately) normally distributed.
b. Construct the 98% confidence intervals for the variance and the standard deviation of SAT scores for all students at this school.