Module Quiz - Module 12: Chi-Square Tests

Quiz Instructions

Questions: 15 multiple-choice questions
Passing score: 11/15 correct (70%)
Format: Auto-graded with immediate feedback
Coverage: All lessons from Module 12
Time: No time limit - work at your own pace
Retakes: You may retake the quiz as needed

What type of data is required for chi-square tests?

A) Quantitative data (measurements) B) Categorical data (counts/frequencies) C) Continuous data only D) Paired numerical data

For a goodness of fit test with 5 categories, what are the degrees of freedom?

A) 5 B) 4 C) 6 D) 3

In a goodness of fit test, if the null hypothesis states that all outcomes are equally likely and you have 240 observations across 4 categories, what is the expected frequency for each category?

A) 240 B) 60 C) 4 D) 80

Which statement about the chi-square distribution is TRUE?

A) It is symmetric and bell-shaped B) It can have negative values C) It is right-skewed and always positive D) It is uniform across all values

For a contingency table with 3 rows and 4 columns, what are the degrees of freedom?

A) 7 B) 12 C) 6 D) 11

In a test of independence, the expected frequency for a cell is calculated as:

A) (Observed - Expected) / Expected B) (Row Total × Column Total) / Grand Total C) Sample size × proportion D) Observed / Sample size

A researcher surveys 400 people (one sample) and records both their age group and political party preference. Which test should be used?

A) Goodness of fit B) Test of independence C) Test of homogeneity D) Two-sample t-test

What is the most critical condition that must be met for all chi-square tests?

A) Sample size must be less than 30 B) All expected frequencies must be at least 5 C) Data must be normally distributed D) Variables must be quantitative

A company samples 100 employees from Office A, 100 from Office B, and 100 from Office C. Each employee rates job satisfaction (High, Medium, Low). Which test should be used?

A) Goodness of fit B) Test of independence C) Test of homogeneity D) ANOVA

What is the key difference between a test of independence and a test of homogeneity?

A) They use different formulas for the test statistic B) Independence has one sample with two variables; homogeneity has multiple samples with one variable C) Independence uses different degrees of freedom D) Homogeneity requires larger sample sizes

A chi-square test of independence yields χ² = 12.5 with df = 4. Using α = 0.05 (critical value = 9.488), what should you conclude?

A) Fail to reject H₀; variables are independent B) Reject H₀; variables are associated C) Accept H₀; variables are definitely independent D) The test is invalid

In a 2×2 contingency table, you have observed frequency O = 30 and expected frequency E = 25 for one cell. What is the contribution of this cell to the chi-square statistic?

A) 5 B) 1 C) 25 D) 0.2

Chi-square tests are ALWAYS:

A) Two-tailed B) Left-tailed C) Right-tailed D) Can be any tail depending on the hypothesis

A researcher tests if a die is fair by rolling it 600 times. What are the null and alternative hypotheses?

A) H₀: The die is fair; Hₐ: The die is not fair B) H₀: The die is not fair; Hₐ: The die is fair C) H₀: All faces have equal probability; Hₐ: At least one face has different probability D) Both A and C are correct

If a chi-square test shows that two variables are associated, what can you conclude?

A) One variable causes changes in the other B) The variables are related, but causation is not established C) The variables are definitely independent D) The test was conducted incorrectly

Safaa Dabagh

Module 12 Quiz: Chi-Square Tests