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AP Statistics

AP Statistics. 13.2 Inference for Two Way Tables. Learning Objective:. Analyze Two Way Tables Using Chi-Squared Test for Homogeneity and Independence. Three Types of Chi-Squared Distributions. Expected Counts= Degrees of freedom (r-1)(c-1) Chi-Squared Test Statistic.

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AP Statistics

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  1. AP Statistics 13.2 Inference for Two Way Tables

  2. Learning Objective: • Analyze Two Way Tables Using Chi-Squared Test for Homogeneity and Independence

  3. Three Types of Chi-Squared Distributions

  4. Expected Counts= • Degrees of freedom (r-1)(c-1) Chi-Squared Test Statistic

  5. Chi-Squared (Homogeneity)- • H₀:the proportion of ________ is the SAME as __________ • Ha: the proportion of ________ is the DIFFERENT than __________

  6. Example 1: Do the boys’ preferences for the following TV programs differ significantly from the girls’ preferences? Use a 5% significance level.

  7. H₀:the boys preference for TV programs is the SAME as the girls • Ha: the boys preference for TV programs is DIFFERENT than the girls • Assumptions: -random sample -all expected counts are ≥ 1 -no more than 20% of the expected counts <5

  8. Chi-Squared Test (Homogeneity) w/ α=0.05 • P(x²>41.08)=0.000000006 • df=3 • Since p< α, it is statistically significant. Therefore we reject H₀. There is enough evidence to say the preference of TV programs for boys is different than girls.

  9. Example 2: The following data is an SRS of 650 patients at a local hospital. Does the effect of aspirin significantly differ from a placebo for these medical conditions?

  10. H₀:the effects of aspirin is the same as the placebo • Ha: the effects of aspirin is different than the placebo • Assumptions: -random sample -all expected counts are ≥ 1 -no more than 20% of the expected counts <5

  11. Chi-Squared Test (Homogeneity) w/ α=0.05 • P(x²>3.70)=0.1573 • df=2 • Since p∡ α, it is not statistically significant. Therefore we do not reject H₀. There is not enough evidence to say the effect of aspirin differs from the placebo.

  12. Chi-Squared (Independence)- • H₀: There is no relationship (association) between ________ and ________. • Ha: There is a relationship (association) between ________ and ________.

  13. Example 3: An SRS of 1000 was taken • Is there a relationship between gender and political parties?

  14. H₀: There is no relationship between gender and political party • Ha: There is a relationship between gender and political party • Assumptions: -random sample -all expected counts are ≥ 1 -no more than 20% of the expected counts <5

  15. Chi-Squared Test (Independence) w/ α=0.05 • P(x²>16.2)=0.0003 • df=2 • Since p< α, it is statistically significant. Therefore we reject H₀. There is enough evidence to say there is a relationship between gender and political party

  16. Example 4: An SRS of 592 people were taken comparing their hair and eye color. Is there an association between hair color and eye color?

  17. H₀: There is no association between hair color and eye color • Ha: There is an association between hair color and eye color • Assumptions: -random sample -all expected counts are ≥ 1 -no more than 20% of the expected counts <5

  18. Chi-Squared Test (Independence) w/ α=0.05 • P(x²>134.98)≈0 • df=9 • Since p< α, it is statistically significant. Therefore we reject H₀. There is enough evidence to say there is an association between hair color and eye color

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