Opdracht 10b
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t-procedures for paired data
t-procedures for independent samples
pooled t-procedures for two independent samples

Two groups, each consisting of 10 teachers of Spanish, followed an
intensive suumer school course in Spanish.  Before and after the
course they underwent a listening test.  The table below gives the
scores before and after the course.  (Data courtesy of Joseph A. Wipf,
Department of Foreign Languages and Literatures, Purdue University.)

Group     After     Before

1         29           30
1         30           28
1         32           31
1         30           26
1         16           20
1         25           30
1         31           34
1         18           15
1         33           28
1         25           20
2         32           30
2         28           29
2         34           31
2         32           29
2         32           34
2         27           20
2         28           26
2         29           25
2         32           31
2         32           29

The data are available in z:\public\share\heeringa\luister.txt.  Read
this ASCII-file in. Define the three columns of the table and choose
the variable names 'group' ('groep'), 'before' ('vooraf') and
'after' ('achteraf').

a. Draw a normal-quantile plot for the scores before and draw a
   second normal-quantile plot for the scores after.

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

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

d. Draw a normal-quantile plot for the group 1 scores before and draw a
   second normal-quantile plot for the group 2 scores before.

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

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 the two populations are not
   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 the two populations are not equal.