STATISTICS 2MA3: Test #2

25 March 1998


Students may bring and use any calculators, one sheet of notes (8.5" x 11", one side only), and any mathematical or statistical tables.

If the tables are in a textbook, elastic bands must be drawn around the remaining pages so that only the tables can be used.

Marks are indicated in the left-hand margin.

[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