Confidence interval/Hypothesis test for standard deviation

[kingwinner]

Homework Statement

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.

Homework Equations

Hypothesis testing/Confidence intervals

The Attempt at a Solution

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 ?

Thank you!

 

[kingwinner]

So my key question here is: Does the similar relationship between confidence interval and hypothesis testing also hold for μ1-μ2 and σ ?

 

[Billy Bob]

So my key question here is: Does the similar relationship between confidence interval and hypothesis testing also hold for μ1-μ2 and σ ?

Yes for two-tailed tests. If you look at the formulas, you can see the test statistic is just a rearrangement of the CI.

For proportion p, the formulas are slightly different, but you can still use the CI method.

One-tailed tests, as with μ, would need "one sided confidence intervals" or "confidence rays" whatever you want to call them.