Understanding hypothesis tests in general: One use of a Chi-square test is to determine whether factors are independent from each other or dependent on each other. For example, consider the following: A marketer, who works for a brewery, has to promote a new beer. She samples 150 people and wants to determine whether there is an association between gender and beer preference. If there is an association, then it means that a persons beer preference can be predicted by
Understanding hypothesis tests in general: One use of a Chi-square test is to determine whether factors are independent from each other or dependent on each other. For example, consider the following:
A marketer, who works for a brewery, has to promote a new beer. She samples 150 people and wants to determine whether there is an association between gender and beer preference. If there is an association, then it means that a persons beer preference can be predicted by knowing the persons gender. The results are:
| Beer preference | ||||
| Gender | Light ale | Lager | Best bitter | Total |
| Male | 20 | 40 | 20 | 80 |
| Female | 30 | 30 | 10 | 70 |
| Total | 50 | 70 | 30 | 150 |
The null hypothesis always says that the factors are independent, i.e. H0: Beer preference and Gender are independent
The alternative hypothesis always says the opposite, i.e. H1: Beer preference and Gender are dependent
The hypothesis test was performed at the 2.5% level of significance and the p-value was found to be 0.0149.
From this you may conclude that ...
a) the data supports a dependency between Gender and Beer preference. Hence we do not accept H0 at the 0.0149% level.
b) the data supports a dependency between Gender and Beer preference. Hence we reject H0 at the 2.5% level.
c) the data does not support a dependency between Gender and Beer preference. Hence we reject H1 at the 2.5% level.
d) the data does not support a dependency between Gender and Beer preference. Hence we do not reject H0 at the 2.5% level.
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