Response to the following problem:
Calculating the Confidence Interval for Standard Deviation
In manufacturing tablets, the quantity of active ingredient that is required to lie within 5 mg of the mean is normally distributed and the required condition is considered to hold if sigma < 1.6. A sample of 35 tablets has a sample standard deviation s = 1.321
(a) Find a 95% confidence interval for sigma.
(b) Formulate and perform a suitable hypothesis test at a significance level of 0.05 to see whether the data provides evidence that the required condition is being met.
(c) Find the power of your test in (b) when sigma = 1.2, 1.4 and 1.6, approximating the answers as best the percentage points in the tables permit.
(d) In the given context how would you answers in (c) help to assess the usefulness of the given data?