MTH - Analysis of Variance (ANOVA)

What is the primary purpose of Analysis of Variance (ANOVA)?

• To compare the variance of a single population

• To compare the means of multiple populations

• To estimate the median of a dataset

• To analyze the mode of the data

In a one-factor ANOVA, what does the null hypothesis state?

• All variances are equal

• All means are equal

• All medians are equal

• None of the means are equal

What distribution does the test statistic in ANOVA follow?

• Chi-squared distribution

• Normal distribution

• F-distribution

• T-distribution

If the calculated F-statistic is close to 1 in a one-factor ANOVA, what conclusion should be made?

• Reject the null hypothesis

• Fail to reject the null hypothesis

• Means are not equal

• Increase sample size

Which of the following conditions would lead to rejecting the null hypothesis in one-factor ANOVA?

• The F-statistic is close to 1

• The F-statistic is much larger than 1

• The variance between groups is small

• The sample sizes are unequal

In two-factor ANOVA, how many factors are tested for their impact on the data?

• One

• Two

• Three

• Four

What is the key difference between one-factor and two-factor ANOVA?

• One-factor ANOVA tests the means, two-factor ANOVA tests the medians

• One-factor ANOVA tests for one independent variable, two-factor ANOVA tests for two

• One-factor ANOVA tests the variances, two-factor ANOVA tests the range

• One-factor ANOVA requires more data

In quality control, how is ANOVA useful?

• It identifies outliers in data

• It ensures all products are identical

• It helps detect differences in manufacturing processes

• It calculates the average product quality

In ANOVA, what happens if the alternative hypothesis is accepted?

• The variances are equal

• All means are equal

• Not all means are equal

• The test is inconclusive

In two-factor ANOVA, the interaction between the two factors is analyzed by:

• Calculating the mean of the data

• Calculating the sum of squares

• Comparing F-statistics for each factor

• Testing the difference in medians