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Chi Squared Test for Independence c 2 Hypothesis Testing • Null Hypothesis, H o – States that the two variables in question are independent of each other. • Alternative Hypothesis, H1 – States that the two variables in question are dependent on each other Chi-Squared Test with GDC • A researcher conjectures that watching football on the weekends is related to gender. Her data gathered is in the frequency distribution chart below. Construct a chi-squared hypothesis test to determine if there is enough evidence to support the researcher’s conjecture. Watch Football on Weekend? Gender Female Male Yes No Chi-Squared Steps • Step 1: Write the null and alternative hypothesis c 2 Chi-Squared Steps c 2 • Step 2: Find the p-value – P-value is the probability value of evidence against the null hypothesis. • Smaller the number the more chance that the two numbers in question really are significantly different • GDC: 2nd Matrix -- Edit – 2 x 2 – Enter Data • P-Value: Stat – Tests -- c 2-Test -- Calculate Chi-Squared Steps c 2 • Step 3: Select an alpha level α – Alpha level represents the chance of making a mistake, the mistake that you reject the null hypothesis when it is actually true • Common Alpha levels are 1%, 5%, 10% • Select α = .01 for this example Chi-Squared Steps c 2 • Step 4: • A) Compare the p-value to the alpha level – P – value > alpha level 2 c • B) Compare the calc against the critical value Chi-Squared Steps c 2 • Step 5: Interpret the comparison 2 • A) If the p-value > alpha level or c calc < CV, DO NOT reject the null hypothesis B) If the p-value < alpha level or c >CV, REJECT the null hypothesis and accept the alternative hypothesis 2 calc