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Hypothesis Testing and Chi Square

Hypothesis Testing and Chi Square. Chi-Square Test ( χ 2 ) determines whether two variables are related. . By Hand.

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Hypothesis Testing and Chi Square

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  1. Hypothesis Testing and Chi Square Chi-Square Test (χ2) determines whether two variables are related.

  2. By Hand.. Melissa conjectures that seat belt usage, for drivers, is related to gender. The data is shown in the contingency table below. Test Melissa’s conjecture using a chi-square hypothesis test at α=0.01.

  3. Write your hypotheses Step 1: Write your null and alternative hypotheses. Ho : (Null) The two variables are independent H1: (Alternative) The two variables are dependent. • H0: Seat belt usage and gender are independent. • H1: Seat belt usage and gender are dependent.

  4. Step 2: Calculate your chi-square statistic • Expand the contingency table and create a total row and column • The values 50,40,25 and 45 are called the observed values. • These are frequencies, NOT percentages

  5. Calculate your chi-square statistic • Find the EXPECTED values: EV50: EV25: EV40: EV45:

  6. Calculating the Chi-Squared Test for Independence

  7. Calculate your chi-square statistic • Put the data side by side into the given table and complete it.

  8. Step 3: Calculate the critical value • A critical value is a number that separates the “reject the null hypothesis” statement from the “accept the null hypothesis” statement. • If the test statistic ( falls to the left of the critical value, the answer is to accept the null hypothesis. • If the test statistic is to the right of the critical value, the answer is to reject the null hypothesis. • The value is not calculated but rather found by using a critical value table • The numbers on the left represent the degrees of freedom (row – 1)(column-1) • The numbers on the top represent the alpha levels. If α= .01, use 1-.01 = .99 as the value in the chart. This is the percent chance that you are wrong. • Match up the degrees of freedom and the p-value to find the critical value.

  9. Step 4: Compare Against the Critical Value • Find this on your formula chart

  10. Compare the chi square value and the critical value. • By hand: • If χ2 < CV ACCEPT the null hypothesis • If χ2 > CV REJECT the null hypothesis • By GDC: • p-value > α, ACCEPT the null hypothesis • p-value < α, REJECT the null hypothesis

  11. By calculator… • https://sites.google.com/site/ibmathstudiesteacherresources/statistics-beyond-the-basics/the-chi-square-hypothesis-test

  12. Example: A survey is taken to determine if music preference is independent of a teenager’s age. The data was collected and organized into a contingency table below. At α = 0.05, determine if the conjecture can be supported.

  13. Write the hypotheses: • Calculate the EXPECTED values • Find χ2

  14. Find the critical value. If by GDC, use the p-value. If by hand, use the CV from the chart. • Compare χ2 to the CV. • Interpret the comparison

  15. Practice • Evelyn hypothesizes that political affiliation, in the United States, is dependent on gender. She collected data by randomly selecting 80 names from the phone directory. Evelyn organized the data in the contingency table below. At α = .05, should the null hypothesis be accepted or rejected.

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