One-way ANOVA Part I – Additional Practice

1. In a completely randomized experimental design, 11 experimental units were used for each of 4 treatments.  Complete the following ANOVA table.

2. In a completely randomized design for ANOVA, the numerator and denominator degrees of freedom are 4 and 25, respectively. The total number of observations must be:

a.   30

b.   29

c.   25

d.   24

3. One-way ANOVA is applied to three independent samples having means 10, 13, and 18, respectively. If each observation in the third sample were increased by 30, the value of the F-statistics would (no

calculation is needed):

a.   increase by 30

b.   remain unchanged

c.   increase

d.   decrease

4. Which of the following is not a required assumption for the analysis of variance?

a.   The variance associated with the random variable must be the same for each population.

b.   The random variable of interest for each population has a normal probability distribution.

c.   Experimental units are independent to each other.

d.   At least 3 populations are under consideration.

5.  One-way  ANOVA  is  performed  on  independent  samples  taken  from  three  normally  distributed populations with equal variances. The following summary statistics were calculated: n1  = 6, x1  = 50, s1  = 5.2, n2  = 8, x2  =  55, s2  = 4.9, n3  = 6, x3  = 51, and s3  = 5.4.

a.   Calculate the grand mean.

b.   Calculate the pooled variance estimate.

6. Use the following data to complete the One-Way ANOVA Summary Table, and to perform the F-test to determine if there is evidence that the population means are not all equal.  Let α = 0.10.

Data:

7. True or False.  The problem in question #6 is balanced.

Use the following narrative to answer questions 8 – 13. The R&D department of a golf ball manufacturer            recently developed three new types of golf balls. They would like to mass-produce the one that travels the         farthest.  Four of each type of golf ball is randomly selected from production.  Twelve golfers were randomly       selected to participate in the experiment and randomly assigned a golf ball to hit.  The travel distances (in yards) were recorded as follows:

The StatTools one-way ANOVA results for this data follow:

8. Identify the Factor, the Response Variable, the Experimental Unit, a Factor Level.

9. Is this an observational study or a designed experiment?

10. Is this problem balanced or unbalanced?

11. What are the relevant null and alternative hypotheses to determine if differences in the driving distances exist between the three types of golf balls?

12. Draw the decision rule for the one-way ANOVA test using a significance level of 0.05.  Make sure it is completely labeled, including the value of the critical point.

13.  Based on the ANOVA results, you should

a. reject the null hypothesis, conclude that the three types of golf balls travel the same distance on average, and stop.

b. not reject the null hypothesis, and conclude that the three types of golf balls travel the same distance on average, and stop.

c. reject the null hypothesis, conclude that the three types of golf balls do not travel the same distance on average, and conduct a post hoc analysis.

d. not reject the null hypothesis, conclude that the three types of golf balls do not travel the same distance on average, and conduct a post hoc analysis.

14. In which of the graphs shown in Figures 1 and 2 below is the “within” group variability larger?

Figure 1

Figure 2