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• Homework due Wednesday!• Criteria A and B due Thursday• Exam Thursday

Hypothesis Testing and Chi Square

Chi-Square Test (χ2) determines whether two variables are related.

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.

Seat Belt Usage

Gender Yes No

Female 50 25

Male 40 45

Write your hypotheses

Step 1: Write your null and alternative hypotheses.Ho: The two variables are independentH1: The two variables are dependent.

• H0: Seat belt usage and gender are independent.

• H1: Seat belt usage and gender are dependent.

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.

Seat Belt Usage

Gender Yes No Total

Female 50 25 75

Male 40 45 85

Total 90 70 160

Calculate your chi-square statistic

• Find the expected values: EV50:

EV25:

EV40:

EV45:

Calculate your chi-square statistic• Put the data side by side into

the given table and complete it.

50 42.1875

25 32.8125

40 47.8125

45 37.1875

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.

Compare the chi square value and the critical value.

• If χ2 < CV, or p-value > α, ACCEPT the null hypothesis

• If χ2 > CV, or p-value < α, REJECT the null hypothesis

By calculator…

Example:

Age

Music Preferences

Country Rap/Blue Rock Total

13-15 8 17 9

16-19 15 8 13

Total

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.

• Write the hypotheses:

• Calculate the EXPECTED values

• Find χ2

• 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

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. Political Affiliation

Gender Democrat Independent Republican

Male 14 3 23

Female 21 6 13