Six Sigma Green Belt Certification Practice Exam

What is the purpose of a chi-squared test?

1. To test two sample means for equality when the variance is unknown but assumed to be equal

2. To compare the observed and expected frequencies of test outcomes

3. To compare a population mean with fixed value when the population follows a normal distribution

4. To compare three or more population means

The correct answer is: To compare the observed and expected frequencies of test outcomes

The purpose of a chi-squared test is to determine whether there is a significant difference between the observed frequencies and the expected frequencies in categorical data. This statistical method is particularly useful for assessing how well the observed data fit into a hypothesized distribution or to test whether two categorical variables are independent of each other. In practice, researchers collect data and categorize them into different groups. The chi-squared test then allows for a comparison between what the researchers would expect if the null hypothesis were true (the expected frequencies) and what they actually observe (the observed frequencies). A significant result indicates that the observed frequencies deviate significantly from what was expected, suggesting there may be a relationship between the variables or that the hypothesized distribution does not fit the data well. Understanding this test is crucial in various fields, including social sciences, biology, and market research, where categorical data is prevalent. Other statistical tests mentioned in the other choices serve different purposes; for example, comparing means assumes continuous data and a specific distribution, while the chi-squared test is suited for categorical data.