Chi Squared Test for Independence

Hypothesis Testing

• Null Hypothesis,– States that there is no significant difference

between two (population) parameters• ie. Two numbers are the same

• Alternative Hypothesis,– States that there is a significant difference

between two (population) parameters • Ie. Two numbers are different

Chi-Squared Test with GDC

• A researcher conjectures that seat belt usage, for drivers, 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.

Seat Belt Usage

Gender Yes No

Female 50 25

Male 40 45

Chi-Squared Steps

• Step 1: Write the null and alternative hypothesis

Chi-Squared Steps

• 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 -- -Test -- Calculate

Chi-Squared Steps

• 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

• Step 4:• A) Compare the p-value to the alpha level– P – value > alpha level

• B) Compare the against the critical value

Chi-Squared Steps

• Step 5: Interpret the comparison• A) If the p-value > alpha level or < CV,

DO NOT reject the null hypothesis

B) If the p-value < alpha level or >CV, REJECT the null hypothesis and accept the alternative hypothesis