Inference for Tables

Catapult Discovery Question: –How does a cat land (feet, side, nose/face)? –Write your predictions in percent. Collect data for the cats –Place actual data in a table –Make table of what you would predict Needed elements of your test –Null and alternative hypothesis, conditions, formula, conclusion.

Food for thought Hypothesis –Think about how one could summarize all null and alternative hypothesis into words Conditions –Think about what the conditions are for the inference using categorical data previously learned Formula –Oh yeah, they gave us a formula chart

Chi-Square Test Basics Formula: Issue of accuracy: Data is from a random sample/event. All individual expected counts are at least 5 (sample size is large enough). H o : observed is the same as what expected H a : observed is different than expected

Chi-Square df =1

Chi-Square df =2

Chi-Square df =3

Chi-Square df =4

Chi-Square df =5

Chi-Square df =8

Chi-Square Goodness of Fit The chi-square(  2 ) test for goodness of fit allows the observer to test if a sample distribution is different from the hypothesized population. H o : the sample distribution is the same as the expected distribution H a : the sample distribution is different from the expected distribution

The type of household for the U.S. population is shown below. The following results are based on a random sample of the community from Dove Creek, Montana. Is there sufficient evidence to conclude that Dove Creek is different than the rest of the United States? Test at the 0.02 level.

H o : the number of household types in Dove Creek are the same as the U.S. H a : the number of household types in Dove Creek is different than the U.S. Expected values table: Chi-square goodness of fit

H o : the number of household types in Dove Creek are the same as the U.S. H a : the number of household types in Dove Creek is different than the U.S. Expected values table: Chi-square goodness of fit

H o : the number of household types in Dove Creek are the same as the U.S. H a : the number of household types in Dove Creek is different than the U.S. Expected values table: Chi-square goodness of fit Given observed counts are from a random sample. Sample is large enough to safely use chi-square since all expected counts are greater than 5.

Formula: df=# of categories – 1 = 4 (no need to rewrite tables again)

Chi-Square Table We reject Ho, since p-value<  there is enough evidence to believe the distribution of household type in Dove Creek is different than the U.S. df=4