Chi-Square Test

What is the main purpose of the Chi-Square Goodness of Fit test?

• To compare observed data with data we would expect to obtain according to a specific hypothesis.

• To determine if there is a significant difference between the means of two groups.

• To assess the relationship between two categorical variables.

• To compare the variance of two samples.

What does the Chi-Square Test of Homogeneity test for?

• The variability within a single sample.

• The difference in variance between two samples.

• Whether different samples come from the same distribution.

• The relationship between two variables within the same sample.

Which of the following is a requirement for both the Chi-Square Goodness of Fit and the Test of Homogeneity?

• The data must be normally distributed.

• The samples must be independent.

• The expected frequency in each category must be at least 5.

• The variables must be continuous.

How do you calculate the expected frequencies in a Chi-Square Goodness of Fit test?

• By dividing the total number of observations by the number of categories.

• By using the mean of the observed frequencies.

• By taking the square root of the observed frequencies.

• By multiplying the sample size by the probability of each category.

Tags

CCSS.HSS.MD.A.2

In the context of a Chi-Square Test of Homogeneity, what does it mean if the p-value is less than the significance level?

• The samples come from distributions with the same variance.

• There is not enough evidence to conclude that the samples come from different distributions.

• There is sufficient evidence to conclude that the samples come from different distributions.

• The samples come from normally distributed populations.

Which of the following scenarios is best suited for a Chi-Square Goodness of Fit test?

• Comparing the mean height of males and females.

• Testing if a die is fair based on the outcomes of several rolls.

• Determining if there is a relationship between gender and preference for a new product.

• Comparing the distribution of blood types among two different ethnic groups.

What is the null hypothesis in a Chi-Square Test of Homogeneity?

• There is no difference between the observed and expected frequencies.

• The observed frequencies match the expected frequencies.

• The samples do not come from the same distribution.

• The samples come from the same distribution.

Which of the following conditions does not apply to the Chi-Square Goodness of Fit test?

• All expected frequencies must be greater than 1.

• No more than 20% of expected frequencies are less than 5.

• Observations must be randomly selected.

• Data must be in the form of counts or frequencies.

In a Chi-Square Test of Homogeneity, how is the chi-square statistic calculated?

• By summing the squared differences between observed and expected frequencies.

• By dividing the sum of squared differences by the expected frequencies.

• By summing the squared differences between observed and expected frequencies, divided by the expected frequencies.

• By multiplying the observed frequencies with the expected frequencies and then summing up.

What is a key difference between the Chi-Square Goodness of Fit test and the Test of Homogeneity?

• The Goodness of Fit test is used for one categorical variable, while the Test of Homogeneity is used for two or more.

• The Test of Homogeneity requires data to be normally distributed, while the Goodness of Fit test does not.

• The Goodness of Fit test can only be used for large sample sizes, while the Test of Homogeneity can be used for any sample size.

• The Test of Homogeneity is used to compare means, while the Goodness of Fit test compares variances.