150
T
T
H
H
E
E
I
I
N
N
F
F
E
E
R
R
E
E
N
N
C
C
E
E
A
A
P
P
L
L
E
E
T
T
This aplet is a very flexible tool for users investigating inference problems. It
provides critical values for hypothesis testing and confidence intervals, and
does this not only quickly but in a visually helpful format.
Before we look at the Inference aplet in detail I am going to take a small
digression to look at a simple inferential problem which can be solved using
only the Statistics and Solve aplets.
Using the Chi2 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. We can do this
in the HOME view using the calculation shown
right (and below), inserting the results into
column C3.
400*COMB(4,C1)*.5^C1*.5^(4-C1) C3
We can now calculate the X
2
value using the
calculations shown right, which places the
individual values into column C4 for inspection
if required.
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