Solving Statistics Retour: 95% Confidence Interval & Hypothesis Test

[Mafer]

I haven't touch statistics for year and now I came back to find I am totally lost.
Here is one of the question that I wish to know how to solve it, in terms of steps, so that I can gain back memory about it.

Part 1:
In a test of a laboratory's measurement of serum cholesterol, 15 samples containing the same known amount (190 mg/dL) of serum cholesterol are submitted for measurement as part of a larger batch of samples, one sample each day over a three-week period. Suppose that the following daily values in mg/dL for serum cholesterol for these 15 samples were reported from the laboratory:

180, 190, 197, 199, 210, 187, 192, 199, 214, 237, 188, 197, 208, 220, 239

Assume that the variance for the measurement of serum cholesterol is supposed to be no larger than 100 mg/dL. Construct the 95 percent confidence interval for this laboratory's variance. Does 100 mg/dL fall within the confidence interval? What might be an explanation for the pattern shown in the reported values?

Part 2:
For the same data, test the hypothesis that the measuring process works - that is, test the hyposthesis that the population mean of the values measured by this process equals 190 versus the alternative hypothesis that the population mean is not equal to 190 mg/dL. Perform the test at the 0.02 significance level.

I know it is a bit too much, but I am really very very lost and depressed, help.

 

[mXSCNT]

These types of questions are straightforward, you just have to look up the appropriate technique (and get familiar with the terminology). According to
http://www.fmi.uni-sofia.bg/vesta/Virtual_Labs/interval/interval6.html :
let S^2 be the sample variance of normally distributed data
let $$\chi^2_{n,a}$$ be the number x such that if X has a $$\chi^2$$ distribution with n degrees of freedom , then P(X < x) = a.
then
$$\left(\frac{n-1}{\chi^2_{n-1,1-a/2}}S^2,\frac{n-1}{\chi^2_{n-1,a/2}}S^2\right)$$
is a 1-a confidence interval for the distribution variance. You can calculate this interval numerically using a table for the $$\chi^2$$ distribution or some stats software.

In part 2, you need to use a one-sample t-test.

If these terms are unfamiliar to you, you just need to review your stats book and look up what you don't remember.