with 1 degree of freedom has a p-value of 0.028 < 0.05Therefore, we reject the null hypothesis of no relationship.Conclusion: there is a relationship between Brand preference and Age.Using the test statistic to test the hypothesis24.83233Life is simple if the null hypothesis is not rejected: If the null were not rejected, these differences you see here don’t exist!This comparison is only meaningful if you reject the null hypothesis of no association!

12•Discuss “strength of association”•Discuss what your finding means in practical terms (or what is the nature of the association between the two variables?)35What rejecting the null hypothesis means in practical terms…n

1337Pepsi is more popular among young people than old people. But be careful when you do it – column percentages vs. row percentages 45.9% of young people surveyed prefer Pepsi61.6% of those who prefer Pepsi are youngRecap: Cross-Tabulation (Chi-square test)1.Test null hypothesis (H0): No association between the variablesusing the chi-square statistic. –If you fail to reject the null hypothesis, then there isno relationship => Stop2.If H0is rejected, determine strength of association using appropriate statistic (phi-coefficient, contingency coefficient, or Cramer's V) – depends on the context3.Draw marketing conclusionsa)Do not reject – end of the line: “There is no association ….”b)Reject – what it means in practical terms38Recap•Hypothesis testing•Cross tabs•Chi-square test•Review Lecture 8 notes and Chapter 1639Key Concepts•Sample vs. populationcharacteristics•Null vs. alternativehypothesis•Cross‐tabulation•Test statistic•P Value•t and chi‐square statistic