chi squared test for independence. hypothesis testing null hypothesis, – states that there is no...
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Chi Squared Test for Independence
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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
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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
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Chi-Squared Steps
• Step 1: Write the null and alternative hypothesis
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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
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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
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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
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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