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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
: There is no relationship between grades awarded and years at
0
school. They are independent.
H
: There is a relationship.
A
If H
is true then the expected frequencies
0
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
values ready for summing as per the
χ
2
(
−
O E
∑
formula
χ
=
2
After first changing to the SYMB view to
register C3, the required total for C3 can be
found in the
g
u
s
i
n
g
t
h
e
C
h
g
u
s
i
n
g
t
h
e
C
h
)
2
.
E
view. In this case, 1.493.
2
2
i
t
e
s
t
i
t
e
s
t
Year
8
9
10
Total
awarded
Year
A
8
25
9
25
10
25
Total
75
299
Grade
awarded
A
B
Total
22
18
40
26
14
40
27
13
40
75
45
120
Grade
B
Total
15
40
15
40
15
40
45
120
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