# Project #17720 - Statistics

1)  Are severe psychiatric disorders related to biological factors? One study used x-ray computed tomography (CT) to collect data on brain volumes for a group of patients with obsessive-compulsive disorders and a control group of health persons. The accompanying list shows sample results (in milliliters) for volumes of the right cordate. Use a 0.01 significance level to test the claim that obsessive-compulsive patients and healthy persons have the same brain volumes.

Obsessive-compulsive patients:

0.308     0.210     0.304     0.344     0.407     0.455     0.287     0.288     0.463     0.334     0.340     0.305

Control group:

0.709     0.476     0.413     0.429     0.501     0.402     0.349     0.694     0.334     0.483     0.460     0.445

a)  A test with two independent samples? Or paired samples?

b) Name the test you will use to test the above claim (don’t actually do the test. You will do a test in c). Please show me your evidence. For example, if you need to do a test (or two) on assumptions before you make your decision, and then use R for the tests. Please show your output as evidence.

c) No matter what is your conclusion in b), please use Mann-Whitney U test with

hand calculation and use the table B.11 (P-value and traditional method)

d)      Please use the test statistics calculated from c) and use large sample Z-approximation method hand calculate for the same hypothesis testing(although it is not large sample in this case).

c)   R code for Mann-Whitney U test and output

2. Two color morphs (green and red) of the same species of sea star were found at Polka Points, North Stradbroke Island. One might suppose that the red color morph is more reliable to predation and, hence, those found might be smaller than the green color morph. The following data are the radial lengths of two random samples of these sea stars (in mm). Are red color morphs significantly smaller than green color morphs at significant level of 0.05?

Red        108         64           80           92           40

Green   102         116         98           132         104         124

State your hypothesis and use Mann-Whitney U test with

a)      hand calculation  and use the table B.11 to find the p-value

b)      use the calculated results from a) and use large sample Z-approximation method for the same hypothesis testing(although it is not large sample).

c)   R code and output

 Subject Mathematics Due By (Pacific Time) 11/24/2013 09:00 am
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