Chi-Square Test Worksheet

Chi-Square Test Worksheet

Read each question carefully and provide your answers in the space provided. Show all your work for calculations.

1. What is the primary purpose of a chi-square test?

2. The formula for the chi-square statistic is χ² = Σ ((O - E)² / E), where O represents the   frequencies and E represents the   frequencies.

3. The number of degrees of freedom for a chi-square goodness-of-fit test is calculated as  , where k is the number of categories. For a test of independence, it is (rows - 1) * (  - 1).

4. Which of the following is NOT an assumption of the chi-square test?

5. A researcher wants to determine if there is a preference for three different brands of soft drinks (A, B, C) among a sample of 150 college students. The observed frequencies are: Brand A = 60, Brand B = 45, Brand C = 45.

a) State the null and alternative hypotheses for this study.

b) Calculate the expected frequencies for each brand, assuming no preference.

c) Calculate the chi-square test statistic.

d) Determine the degrees of freedom.

e) If the critical value for χ² at α = 0.05 with the calculated degrees of freedom is 5.991, what is your conclusion?

6. A company wants to know if there is a relationship between employee satisfaction (Satisfied, Neutral, Dissatisfied) and their department (Sales, Marketing, HR). They collected the following data:

Observed Frequencies:

Satisfied | Neutral | Dissatisfied

Sales: 50 | 20 | 10

Marketing: 30 | 15 | 5

HR: 20 | 10 | 10

a) State the null and alternative hypotheses.

b) Calculate the degrees of freedom for this test.

c) Explain how you would calculate the expected frequency for 'Sales' and 'Satisfied'. (You do not need to calculate all expected frequencies, just explain the process for one cell).