# Questions about the chi-square (X^2) statistic

True or False

1. The X^2 test statistic is a random variable that is based on frequencies.

2. The chi-square test for independence is a non-parametric statistical test because no parameters are estimated

3. Observed frequencies in a chi-square goodness-of-fit test for normality may be less than 5 or even 0 in some cells, so long as the expected frequencies are large enough.

4. If two variables are independent you would expect the X^2 test statistic to be close to zero.

5. The null hypothesis for a chi-square contingency test of independence for two variables always assumes the variables are independent.

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#### Solution Preview

1. The χ2 test statistic is a random variable that is based on frequencies.

True. There are two kinds of chi-square tests:

goodness-of-fit (comparing frequencies of one variable to theoretical or expected frequencies)

test of independence (comparing frequencies of one variable to frequencies of a second variable)

2. The chi-square test for ...