© 2011 BFW Publishers
The Practice of Statistics, 4/e- Chapter 11
We are looking for a difference in the proportion cars choosing each of the three lanes, so
the alternative hypothesis is that the population distribution of the categorical variable is
not equal for at least one of the three values (the alternative hypothesis includes the
possibility that the two proportions are equal to each other, but different from the third).
Choice a is about tests of means, choices b and c make reference to observed counts,
which are not involved in conditions required for chi-square procedures.
For a chi-square test of homogeneity, the null hypothesis is that the distribution of a
categorical variable is the same for two or more different populations.
There are three
random samples in this setting from three distinct populations.
Degrees of freedom for any chi-square test involving a 2-way table is
number of rows
number of columns
Expected counts in a two-way table
Since the component for midnight/within specifications is a small fraction of the total
chi-square statistic (0.090), the observed and expected counts must be close to equal.
Each component of a chi-square statistic is
for the given cell.
The 2 x 3 table produces a chi-square statistic with 2 degrees of freedom, thus the
value is much less that 0.05, providing strong evidence against the null hypothesis that
accident type and age are independent.
A chi-square test on a 2 x 2 table is equivalent to a two-sided two-proportion
1 is the square of the standard normal distribution.
, and the resulting
value is the same.
State: We are testing the hypothesis
: The proportion of allergy sufferers born during each
season of the year matches the proportion of the general population born during each season,
: The proportion of allergy sufferers born during each season of the year does not
match the proportion of the general population born during each season.
We will use a
significance level of
The procedure is a chi-square goodness-of-fit test.
: the data come from a simple random sample of 500 people who are
allergic to dust mites.
Large sample size
: Expected counts are: Winter: 150; Spring: 110;
Summer: 120; Fall: 120
all are at least 5.
: Randomly-selected allergy sufferers
should be independent; and there are surely at least 10 x 500 people who suffer from dust mite
value = 0.0028.