23
T
T
H
H
E
E
E
E
X
X
P
P
E
E
R
R
T
T
:
:
C
C
H
H
I
I
2
2
T
T
E
E
S
S
T
T
S
S
&
&
F
F
R
R
E
E
Q
Q
U
U
E
E
N
N
C
C
Y
Y
T
T
A
A
B
B
L
L
E
E
S
S
We will start with a small digression to look at a simple inferential problem which can be solved using only
the Statistics and Solve aplets.
Using the Chi
2
test on a frequency table
“Four coins are tossed 400 times and the number of heads noted for each toss.
The results are shown below. Using the Chi
2
test at a 5% level of confidence,
indicate whether the coins may be biased.”
Number of heads
0
1
2
3
4
Frequency
32 112 158 90 8
We would expect that for an un-biased set of coins the distribution would be binomial. Our hypotheses are:
H
0
:
The number of heads is binomially distributed (n=4 & p=0.5)
H
A
:
The number of heads is
not
binomially distributed (n=4 & p=0.5)
Begin by entering the data into the first two columns
of the Statistics aplet (right).
We now need to calculate the expected values based on our null
hypothesis. The expected values are based on the assumption that the
results are binomially distributed with n=4 and p=0.5.
We can do this in the
HOME
view using the calculation shown right
(and below), inserting the results into column
C3
using the
button.
400*COMB(4,C1)*.5^C1*.5^(4-C1) C3
We can now calculate the
X
2
value as the sum of the values in column
C4
using the
∑
LIST
function. The calculations are shown right, placing
the individual values into column
C4
for inspection if required and then
finding the sum of the column.
The values can be seen by changing to the
NUM
view.
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