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.