Chi-Square Test Section 12.1.

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Chi-Square Test Section 12.1

Categorical Variables Based on observations Univariate – single categorical variable Example: Sample 100 people & ask if they agree or disagree with a question. Bivariate – uses two categorical variables Example: Sample 100 people & ask if they are male/female and what political party they support.

One-Way Frequency Table - univariate Democrat Independent Republican Data Vertical One-Way Table Horizontal One-Way Table   Freq. Democrat 4 Republican 6 Independent 2   Democrat Republican Independent Freq. 4 6 2

Goodness of Fit Test Used to measure the extent to which the observed counts differ from the expected counts. K = # categories of a catagorical variable Df = k – 1 Test Statistic:

Assumptions Observed Values are based on random Samples Sample size is large – each cell count is at least 5.

Hypotheses Ho: State each proportion’s hypothesized value. HA: At least 1 of the proportions differ from the hypothesized value.

It uses the Chi-Square Chart Positively Skewed Uses d.f. On calculator!

Is there a preference in type of car?   Freq. Expected SUV 27 Truck 25 Sedan 29 Sports 19 P1=proportion who prefer a SUV P2=proportion who prefer a truck p3=proportion who prefer a sedan P4=proportion who prefer a sports car Assumptions: Random Samples & all cell counts are at least 5. Use a Chi-Square goodness of fit Test P-val = xcdf(2.24,∞, 3)=0.52

A researcher believes that the number of homicides crimes in CA by season is uniformly distributed. To test this claim, you randomly select 1200 homicides from a recent year and record the season when each happened. Season Freq Spring 312 Summer 299 Fall 297 Winter 293

Results from a previous survey asking people who go to movies at least once a month are shown in the table below. To determine whether this distribution is still the same, you randomly select 1000 people who go to movies at least once a month and record the age of each. Are the distributions the same? Age Survey Freq 2 - 17 26.70% 240 18 - 24 19.80% 214 25 - 39 19.70% 183 40 - 49 14% 156 50+ 207

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