Chapter 21

Hypotheses for goodness of fit

1. Recognize and state a claim about population proportions for categories of a categorical variable in a population.
2. Given claimed proportions of categories in a population, state the null and alternative hypothesis corresponding to that claim.
3. Explain why the alternative hypothesis of a “the population proportions equal the specified values” null hypothesis does not specify precisely which population proportions, if any, differ.

Expected counts and chi-square statistic

1. Given a one-way table of counts and null values for population proportions, compute the expected count for each category.
2. Compute the deviation between the observed counts in a sample and the expected counts under the null model.
3. Compute the \(\chi^{2}\)-statistic given observed counts and population proportions.
4. Recognize the Greek letter \(\chi\) (“chi”, pronounced “ki” as in “kite”) as the Greek analog to the Roman letter \(x\).
5. Compute the \(\chi^{2}\)-statistic from observed counts and null proportions using xchisq.test from mosaic.

The chi-square test for goodness of fit

1. Explain why it is more appropriate to call the \(\chi^{2}\) “goodness-of-fit” test a “lack-of-fit” test.
2. Interpret the output of xchisq.test in terms of a \(\chi^{2}\) lack-of-fit test.
3. Use the output of xchisq.test to test a hypothesis about the proportions of some category in a population.

Interpreting significant chi-square results

1. Construct simultaneous confidence intervals for the population proportions of a categorical variable using gf_pop_props from MUsaic.
2. Interpret the output of gf_pop_props.
3. State the implicit null hypothesis tested by checking for inclusion of a null population proportion in a confidence interval returned by gf_pop_props.

Conditions for the chi-square test

1. State the assumptions on a sample for the \(\chi^{2}\) statistic to follow a \(\chi^{2}\) distribution.