```Laboratory Exercise 3: T-Tests
------------------------------

paired t-tests
single sample t-tests
unpaired t-tests

Two groups of ten teachers French attended an intensive summerschool
in French.  They had to take an auditory exam before and after the
course. The table below shows their scores before and after.

Group     Before   After

1        32       34
1        31       31
1        29       35
1        10       16
1        30       33
1        33       36
1        22       24
1        25       28
1        32       26
1        20       26
2        30       36
2        20       26
2        24       27
2        24       24
2        31       32
2        30       31
2        15       15
2        32       34
2        23       26
2        23       26

Put the data into a table. Define three columns of the table and
choose names for the columns like 'group', 'before' and 'after'.

a. Draw a histogram for the 'scores before' and a histogram for the
'scores after'.

b. Give a 90%-confidence interval for the average increase of the
scores of the auditive exam, an increase due to attending the
summerschool. Do not differentiate between group 1 and group 2.

c. Is the increase in scores significant? Formulate the appropriate
H_0 (Hypothesis zero) and H_a. Do not distinguish between
group 1 and group 2.

d. Draw a histogram for the 'scores before' of group 1. Do the same
for the 'scores before' of group 2.

e. Give a 90%-confidence interval for the difference in averages of the
'scores before' of both group 1 and group 2. Assume that the
standard deviations of both populations are not equal.

f. Is there a significant difference between the average 'score
before' of group 1 and the average 'score before' of group 2?
Formulate the appropriate H_0 and H_a.  Assume that the standard
deviations of both populations are not equal.

Time permitting, you might try the following:

g. Give a 90%-confidence interval for the difference in averages of
the 'score before' of group 1 and the 'score before' of group
2. Assume that the standard deviations of both populations are
equal.

h. Is there a significant difference between the average 'score
before' of group 1 and the average 'score before' of group 2?
Formulate the appropriate H_0 and H_a.  Assume that the standard
deviations of both populations are equal.

```