Exploring the Chi-Square Test for Homogeneity

This video tutorial introduces the chi-squared test for homogeneity, explaining how to set up null and alternative hypotheses to determine if two groups have similar distributions for a variable. The example used is the preference for subject domains between left-handed and right-handed people. The video covers sampling, data collection, calculating expected values, and computing the chi-squared statistic. It also explains how to determine degrees of freedom and interpret the p-value to decide whether to reject the null hypothesis.

What does the chi-squared test measure in terms of group comparison?

• Difference in mean values

• Correlation between variables

• Similarity in variance

• Similarity in distribution

What is the null hypothesis in the context of comparing left-handed and right-handed individuals' subject preferences?

• Left-handed individuals prefer humanities

• Right-handed individuals prefer STEM subjects

• No difference in preferences between the groups

• Preferences differ between the groups

How many right-handed individuals preferred STEM subjects?

• 60

• 24

• 15

• 30

Which subject had the highest preference among left-handed individuals according to the data?

• Both equally

• STEM

• Neither

• Humanities

What should the expected number of left-handed individuals preferring STEM be under the null hypothesis?

• 16

• 24

• 10

• 40

What is the minimum expected count per cell required to properly conduct a chi-squared test?

• 15

• 10

• 1

• 5

What condition checks that the sample is no more than 10% of the population?

• Sample size condition

• Minimum expected condition

• Independence condition

• Random condition

How is the chi-squared statistic calculated?

• Observed * Expected / (Observed + Expected)

• (Observed - Expected)^2 / Expected

• (Observed / Expected)^2

• (Expected - Observed)^2 / Observed

What are the degrees of freedom for a chi-squared test with 3 rows and 2 columns?

• 6

• 4

• 2

• 1

If the p-value is less than the significance level, what is the appropriate action regarding the null hypothesis?

• Recalculate the p-value

• Accept the null hypothesis

• Increase the sample size

• Reject the null hypothesis