Confidence interval/Hypothesis test for standard deviation
1) A random sample of 26 students who are enrolled in College A was taken and their SAT scores were recorded. The sample mean is 548 and the sample standard deviation is s=57. Assume population is normally distributed.
a) Find a 98% confdience interval for the standard deviation of SAT scores of all the students who are enrolled in College A.
b) The principal of College A claims that the standard deviation of SAT scores of studnets in her college is 48. Does the data support the principal's claim? Justify.
I am OK with part a, but have some concerns about part b.
For part b, is it a hypothesis testing (H_o: σ^2 = 48^2, H_a: σ^2 ≠ 48^2) problem or is it a confidence interval problem? Can it be answered solely by using confidence interval? I have seen a theorem saying that "reject H_o: μ=μ_o at the level alpha if and only if μ_o falls outside the 100(1-alpha)% confidence interval for μ", but that's just for μ. Does it also hold for μ1-μ2 and σ ???
[note: also under discussion in sos math forum]