# ANOVA and hypothesis testing problems

ANALYSIS OF VARIANCE (ANOVA)

NOTES

The F Distribution and it is also applied when we want to compare several population means simultaneously. The simultaneous comparison of several population means is called analysis of variance (ANOVA). The populations must be normal, and the data must be at least interval-scale. What are the characteristics of the F-distribution?

1. There is a family of F distributions. A particular member of the family is determined by two parameters: the degrees of freedom in the numerator and the degrees of freedom in the denominator.

2. The F distribution is continuous.

3. The F distribution cannot be negative.

4. It is positively skewed.

ANOVA Assumptions

1. The populations are normally distributed.

2. The populations have equal standard deviations (σ).

3. The samples are selected independently.

Questions

1. A total of 16 observations was selected from four populations. A portion of the ANOVA table follows.

Source Sum Degrees Mean

of Variation of Squares of Freedom Square F

Treatments 400

Error

Total 1500

Complete the table and answer the following questions. Use the .05 significance level.

a. How many treatments are there?

b. What is the total sample size?

c. What is the critical value of F?

d. Write out the null and alternative hypotheses.

e. Make a decision about the null hypothesis. Give a reason for your decision. What is you conclusion?

2. Suppose you are using ANOVA to study some phenomenon. There are five treatment levels and a total of 30 people in the study. Each treatment level has the same sample size.

Source of Variation SS DF MS F

Treatment 583.39

Error 972.18

Total 1555.57

Complete the table and answer the following questions. Use the .05 significance level.

a. How many treatments are there?

b. What is the total sample size?

c. What is the critical value of F?

d. Write out the null and alternative hypotheses.

e. Make a decision about the null hypothesis. Give a reason for your decision. What is you conclusion?

3. Suppose you are using ANOVA to study some phenomenon. There are three treatment levels and a total of 17 people in the study. Complete the following ANOVA table.

Source of Variation SS DF MS F

Treatment 29.64

Error 68.42

Total

Complete the table and answer the following questions. Use the .05 significance level.

a. How many treatments are there?

b. What is the total sample size?

c. What is the critical value of F?

d. Write out the null and alternative hypotheses.

e. Make a decision about the null hypothesis. Give a reason for your decision. What is you conclusion?

#### Solution Summary

The solution provides step by step method for the calculation of test statistic for ANOVA . Formula for the calculation and Interpretations of the results are also included.