```

name _______________________________________________  version 1
FINAL EXAM - STATISTICS 3093 - 1996 DECEMBER
OPEN BOOK -- NOTES & CALCULATORS ALLOWED -- TIME: 3 HOURS

QUESTION ONE    [24/80]
0   0 1
1   4          The largest number of this stem
2   2 8        and leaf diagram is  6.4
3   0 2        Calculate from this data the
4   0 4 7      quantities requested:
5
6   4

FIRST, SECOND & THIRD QUARTILES _______ _______ _______

MEAN (AVERAGE)                           ______________

STANDARD DEVIATION                       ______________

95% CONFIDENCE INTERVALS

FOR MEDIAN               ____________ TO __________

FOR MEAN                 ____________ TO __________

QUESTION TWO     [8/80]

Each of a class of 16 is given a different block of digits from
the same random number generator.    All 16 test the generator
using a chi-square test at alpha=0.10 ((NOT 0.05))  Assume all
their work is correct.  Even though the generator is OK some
of the class will probably reject it.   What is ---

a) The expected number of rejections                     __________

b) The (small) probability that nobody rejects it        __________

c) The probability that (exactly) one person rejects it. __________

QUESTION THREE   [8/80]

(A) Invent two sets of data:
i)  One OBVIOUSLY suitable for techniques using a standard deviation
(such as confidence intervals for the mean).
ii) One OBVIOUSLY NOT suitable for techniques using a std. dev.

(B) Invent two scatter plots:
i)  One OBVIOUSLY suitable for regression (least squares) techniques.
ii) One OBVIOUSLY NOT suitable for regression techniques.

```

```
page 2   stat 3093
name _______________________________________________  version  1

QUESTION FOUR   [24/80]
This table describes a simple linear regression
(least squares fit). Fill in the missing numbers.

Hint: Since two points determine a line, you can solve
for the fitted line after finding any 2 points on it.
After that, the rest is straightforward.

X                1      2      3      4      5

Y               18     18  _____     16     34

FITTED LINE  _____  _____  _____  _____     27

RESIDUAL         3  _____     -2     -8      7

Calculate the quantity which is an analog of the standard
deviation describing the size of a "typical" residual.
(Minitab reports this quantity as "s".)

QUESTION FIVE   [16/80]
X is distributed as follows: P{X=1}= 0.3 , P{X=2}= 0.5 , P{X=3}= 0.2
Evaluate (as a number) the expectation and variance of 60/X
X              1    2    3
Probability     0.3  0.5  0.2
60/X           60   30   20

Y is distributed the same way as X, and X and Y are independent.
Evaluate (as a number) the expectation and variance of

(a)        60/X  +  30/Y                        _________

(b)        60/X  +  30/X                        _________
((Look carefully to see which are Y`s and which are X`s.))
```