STATISTICS 2MA3

TEST #2 • 2002-03-07

Instructions

Aids permitted: any calculators, any tables and one sheet of notes (8.5" x 11", one side only).
Marks: Q1= 10, Q2 = 10, Q3 = 10, Q4 = 10.

Questions

1. (a) Write a note about the person after whom the Poisson Distribution is named, giving at least five interesting facts about his life and work.
(b) Define the following terms: parameter, sample, statistic, sampling distribution.

2. (a) Let X be the score on the upturned face after a fair 6-sided die is rolled. Find the mean and variance of X.
(b) Let Y be the total score obtained by rolling 10 such dice independently. Find the mean and variance of Y. Hence find (at least approximately) the probability that Y > 45 and the probability that Y > 60.

3. Display the following data on a histogram (density scale) and, for comparison, superimpose a Poisson distribution with the same mean. Are the data over-dispersed, under-dispersed or Poisson distributed?

```3 6 3 6 4 4 2 5 3 6 2 3 6 5 1 5 3 3 5 3
```

4. The following data are the differences between Level 2 and Baseline heart rate for patients treated with propanolol in the nifedipine study from Assignment 2.

```> (Lv2hrtrt-Bashrtrt)[Trtgrp=="P"]
 4 NA 5 NA 5 -8 NA -2 8 0 12 13 0 0 NA NA
```

(a) Is there evidence that the mean difference is not zero? Answer this question by computing a two-sided 95% confidence interval for the mean difference. State any assumptions made.
(b) Answer the same question using the number of positive differences. Why should the zero differences be omitted from this analysis?