(you don't have to answer all parts, just most, tip will be given if all)

I'd prefer the answer in MS Word with Equation Editor, but other
reasonable options are definitly acceptable.

Please have this question completed by 11:00 AM on the 31st, as I need
to understand this before my test.

(PDF file here for details: http://7ds.gotdns.org/dl/hw8.pdf)

A sample size 9 from a normal distribution sigma^2 = 25 is used to test 
H0: = 20 
H1: = 28 
The test statistic used is the sample mean, X bar. Let us agree to
reject H0 in favor of H1 if the observed value of sigma^2 is greater
than 25.
(a) If H0 is true, what is the distribution of X bar ? 
(b) In the diagram below, shade the region whose area is alpha (or
just describe where its supposed to be shaded).
(c) Find alpha. Remember that is computed under the assumption that H0 is true. 
(d) If H1 is true, what is the distribution of X bar? 
(e) In the diagram below, shade (or describe where its supposed to be
shaded) the region whose area is beta. Remember that beta is computed
under the assumption that H1 is true.
(f) Find beta. 
(g) Find the power of the test. 
(h) If the sample size is increased, the standard deviation of X bar
will decrease. What is the geometric effect of this on the two curves
of the figure below?
(i) If the sample size is increased but the critical point is not
changed, what will be the effect on alpha and beta?