Inference for Tables Chi-Square Tests Ch. 11.

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Inference for Tables Chi-Square Tests Ch. 11

Food for thought Hypothesis Conditions Formula 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 Ho: observed is the same as what expected Ha: observed is different than expected Formula: Conditions: Data is from a random sample/event. All individual expected counts are at least 5 (sample size is large enough). Population is at least 10 times the sample size

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(c2) test for goodness of fit allows the observer to test if a sample distribution is different from the hypothesized population. Ho: the sample distribution is the same as the expected distribution Ha: 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.

Chi-square goodness of fit (or χ2 GOF, for short) Ho: the number of household types in Dove Creek is the same as the U.S. Ha: they are different Expected values table:

Chi-square goodness of fit (or χ2 GOF, for short) Ho: the number of household types in Dove Creek is the same as the U.S. Ha: they are different Expected values table:

Chi-square goodness of fit (or χ2 GOF, for short) Ho: the number of household types in Dove Creek is the same as the U.S. Ha: they are different Expected values table: Given random sample. Exp. counts > 5, ∴ large sample At least 4110 households in pop.

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

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