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A teacher wishes to decide, at the 5%
level of significance, whether the
performance in a problem solving test
is independent of the students’ year
at school. The teacher selected 120
students, 40 from each of Years 8, 9
& 10, and graded their performance
in a test as either A or B.
The table above right shows the results.
The hypotheses being tested are:
H
0
: There is no relationship between grades awarded and years at
school. They are independent.
H
A
: There is a relationship.
If H
0
is true then the expected frequencies
should be those in the table on the right.
Enter the observed and expected frequencies
into columns
C1
and
C2
of the Statistics aplet.
In the
HOME
view, perform the calculation
shown right. This calculates the individual
2
χ
values ready for summing as per the
formula
(
)
2
2
O
E
E
χ
−
=
∑
.
After first changing to the
SYMB
view to
register
C3
, the required total for
C3
can be
found in the
view. In this case, 1.493.
Grade
awarded
Year
A B
Total
8
22 18
40
9
26 14
40
10
27 13
40
Total
75 45
120
Grade
awarded
Year
A B
Total
8
25 15
40
9
25 15
40
10
25 15
40
Total
75 45
120
