## Old Final: Stat3093 August 1996

```
name ___________________________________________________________

QUESTION ONE
0   1 1
1   5          This stem and leaf diagram
2   2 4 9      is made from data consisting
3   3          of one or two digit integers.
4   1 2
5              Calculate the quantities
6   4 8        requested below:

FIRST, SECOND & THIRD QUARTILES _______ _______ _______

MEAN (AVERAGE)                           ______________

STANDARD DEVIATION                       ______________

QUESTION TWO
Classify these plots as suitable or unsuitable for regression
A                    B                     C         *   *
|         *          |* *                  |   *  *
|       *            |     * *             | *   *    * * *
|     *              |         *           |  * *  *   *
|   *                |          *   *      |  *   *
| *              *   |                     | *
+------------------  +------------------   +----------------

D *   *              E             *   *   F              *
|     *              |          *          |        *
|       * *          |        *       *    |    *
|         *          |      *   *      *   |  *
|                    |     * *  *  *       | *
|                *   |   **  *             |*
+------------------  | * *                 +----------------
+-------------------

QUESTION THREE
Given independent random variables, X, Y, with
E{X} = 111,   E{Y} =  63
V{X} =  12,   V{Y} =  40
Evaluate the expectation and standard deviation of
3 ( 3X/4 + 4Y/5 ) / 5

QUESTION FOUR
It is said that more moss grows on the north sides of of trees.
Assume  60 trees are classified as North, South, East, or West
according to which side shows the most moss.  This is condensed
to a summary of three catagories:
North    South  East+West    Total
17       19       24         60

(a) State the appropriate null hypothesis.
(b) Perform an appropriate hypothesis test.
(c) The chi_square table value for testing at alpha = 5% ___________
(d) Is the null hypothesis rejected at 5%?               YES__  NO__
(e) State a conclusion in terms of the original
problem, i.e. the moss, in one or two sentences
```

William Knight / Math Dept / University of New Brunswick `knight@unb.ca`