Using Your TI83/84 Calculator for Hypothesis Testing:
The ChiSquare GoodnessofFit Test
Dr. Laura Schultz
If births were uniformly distributed across the week, we would
expect that about 1/7 of all births occur during each day of the
week.
How closely do the observed number of births fit this
expected distribution?
The chisquare goodnessoffit test is used
to determine whether an observed frequency distribution is
significantly different from the expected distribution, or how
“good” (sic) the two distributions fit each other.
If we were only
interested in one day of the week, we could conduct a 1proportion
z
test.
However, because we have seven hypothesized proportions,
we need to conduct a test that considers all of them together and
gives an overall indication of whether the observed distribution
differs from the expected one.
The chisquare goodnessoffit test is just what we need.
Let’s
consider the frequency distribution of all 2003 New Jersey births by day of the week.
If you have a TI84 Plus calculator, there is a builtin chisquare goodnessoffit (GOF) test.
If not,
you will need to follow a somewhat more complicated procedure.
I will provide instructions for
both calculator models; use whichever method applies to your calculator.
χ
2
GoodnessofFit Test for the TI83 Calculator
1. Start by clearing
L
1
,
L
2
, and
L
3
.
We will need all three lists in order to compute the
χ
2
test
statistic.
2. Enter the observed number of births for each day of the week into
L
1
.
(The general procedure is
to put observed frequencies in
L
1
.)
3. Now we need to compute the expected frequency for each day of the week.
Because we are
hypothesizing that births are uniformly distributed, we calculate the expected frequency as
E
=
n
/
k
, where
n
is the total number of trials (births, in this case) and
k
is the
number of different categories (days of the week, in this case).
For this
example,
E
= 116823/7 = 16689.
We will use this expected frequency for each
day of the week.
(If we had been hypothesizing unequal frequencies, you
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 Fall '07
 Jerome
 Statistics, ChiSquare Test, Null hypothesis, Statistical hypothesis testing, births, ChiSquare GoodnessofFit Test, goodnessoffit test, Dr. Laura Schultz

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