Chi-Square Test and Hypothesis Testing

This video tutorial explains the test of homogeneity using a chi-square distribution. It covers the purpose of the test, which is to determine if two populations have the same distribution. The video outlines the procedure for calculating the test statistic, including using a TI-84 calculator to find expected values. An example is provided comparing the living arrangements of male and female college students. The tutorial concludes with interpreting the results and making a conclusion based on the p-value and level of significance.

What is the primary purpose of the test of homogeneity?

• To calculate the mean of a population

• To test the variance of a population

• To determine if a population fits a given distribution

• To compare two population distributions

Which test is expanded by the test of homogeneity?

• One-sample t-test

• Paired t-test

• ANOVA

• Two-proportion z-test

What is the null hypothesis in a test of homogeneity?

• The variance of the two populations is equal

• The mean of the two populations is equal

• The distributions of the two populations are the same

• The distributions of the two populations are different

How are the degrees of freedom calculated in a test of homogeneity?

• Number of columns minus one

• Number of categories minus one

• Total number of observations minus one

• Number of rows minus one

In the example problem, what is the level of significance used?

• 0.15

• 0.10

• 0.05

• 0.01

What is the first step in using a calculator for the chi-square test?

• Enter the data into matrix B

• Graph the chi-square distribution

• Calculate the p-value

• Enter the data into matrix A

What does a low p-value indicate in the context of hypothesis testing?

• The null hypothesis is accepted

• The null hypothesis is rejected

• The test is inconclusive

• The alternative hypothesis is rejected

What is the chi-square test statistic approximately in the example problem?

• 5.13

• 15.13

• 10.13

• 20.13

What is the conclusion if the p-value is less than the level of significance?

• Reject the alternative hypothesis

• Accept the alternative hypothesis

• Reject the null hypothesis

• Accept the null hypothesis

What can the test of homogeneity not determine?

• The p-value

• The chi-square statistic

• Whether distributions are the same

• How distributions differ