Chi-Square Test Worksheet

Chi-Square Test Practice

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

1. The Chi-square test is a statistical test used to examine the difference between observed and   frequencies.

2. The symbol for the Chi-square statistic is  .

3. When performing a Chi-square test for goodness-of-fit, the null hypothesis states that there is   significant difference between the observed and expected distributions.

4. A company claims that its new energy drink helps improve focus. They surveyed 100 students: 40 reported improved focus, 35 reported no change, and 25 reported decreased focus. If the company claims an equal distribution of outcomes, perform a Chi-square goodness-of-fit test at a 0.05 significance level to see if the observed distribution differs significantly from the expected uniform distribution. State your null and alternative hypotheses, calculate the Chi-square statistic, find the critical value, and state your conclusion.

5. The degrees of freedom for a Chi-square goodness-of-fit test are calculated as (number of categories - 1).

6. A large Chi-square test statistic value indicates a good fit between observed and expected frequencies.

7. A study investigated the relationship between gender and preference for three types of movies: Action, Comedy, and Drama. The results are shown in the table below. At a 0.01 significance level, determine if there is a significant association between gender and movie preference. State your hypotheses, calculate the Chi-square statistic, find the critical value, and state your conclusion.

Observed Frequencies:

8. What is the primary purpose of a Chi-square test for independence?