[13] 1. Analyse the following data appropriately. State any assumptions you make and do what you can, including descriptive statistics and graphical methods, to check the validity of the assumptions. Your analysis should include: box plots, an F test, and a t-test. State your conclusions in terms of P-values.
The data below are measurements of total heart weight (THW) from a group of 10 normal males and a group of 10 males with left-heart disease (LHD), taken at autopsy at a particular hospital.
LHD:
450
760
325
495
285
450
460
375
310
615
Normal:
245
350
340
300
310
270
300
360
405
290
[13] 2. Draw a graph of the Bin(n,p) probability density function for p = 0.5. Given a single observation from a Bin(n,p) distribution, find a test for the hypothesis that p = 0.5 against a two-sided alternative. Make the size of the test as close as possible to 5%. Show that the power of the test is given by
g(p1) = (1 - p1)6 + p1 6.
Draw a graph of the power. What does the power curve tell us about the test?
[5] 3. Most North American journals will not publish the result of a study unless the null hypothesis has been rejected at the 5% level of significance. What are the implications of this policy if many different laboratories are studying the same treatment and the treatment happens to be no different from the control? Would this situation be better if all the tests were two-sided?
[5] 4. Give a 99% confidence interval for the odds ratio in the following contingency table.
Treatment:
Exptl.
Control
Remission:
Y
75
44
N
53
73