The Expert: Chi 2 Tests & Frequency Tables - HP 39gs Master Manual

T E : C
T E : C
H E X P E R T
H E X P E R T
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.
2
Using the Chi 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
indicate whether the coins may be biased."
Number of heads
Frequency
We would expect that for an un-biased set of coins the distribution would be binomial. Our hypotheses are:
H : The number of heads is binomially distributed (n=4 & p=0.5)
0
H : The number of heads is not binomially distributed (n=4 & p=0.5)
A
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
(and below), inserting the results into column
400*COMB(4,C1)*.5^C1*.5^(4-C1) C3
We can now calculate the X
using the function. The calculations are shown right, placing
C4 ∑LIST
the individual values into column
finding the sum of the column.
The values can be seen by changing to the
& F
2
2 & F
H I T E S T S
H I T E S T S
0 1
32 112
view using the calculation shown right
using the
C3
value as the sum of the values in column
2
for inspection if required and then
C4
NUM
R E Q U E N C Y T A
R E Q U E N C Y T A
2 test at a 5% level of confidence,
2 3 4
158 90 8
button.
view.
147
B L E S
B L E S
23