Question

Please help with the following multiple choice

1. In the one-way ANOVA where there are k treatments and n observations, the degrees of freedom for the F-statistic are equal to, respectively:

a. n and k. b. k and n. c. n − k and k − 1. d. k − 1 and n − k.

2. In ANOVA, the F-test is the ratio of two sample variances. In the one-way ANOVA (completely randomized design), the variance used as a numerator of the ratio is:

a. mean square for between treatments. b. mean square for within treatments. c. total sum of squares. d. None of these choices.

3. The number of degrees of freedom for the denominator in one-way ANOVA test involving 4 population means with 15 observations sampled from each population is:

a. 60 b. 19 c. 56 d. 45

4. For which of the following is not a required condition for ANOVA?

a. The populations are approximately normally distributed. b. The population variances are equal. c. The samples are random and independent. d. All of these choices are required conditions for ANOVA.

5. One-way ANOVA is applied to independent random samples taken from four approximately normally distributed populations with equal variances. If the null hypothesis is rejected, then we can infer that

a. all population means are equal. b. all population means differ. c. at least two population means are equal. d. at least two population means differ.

6. In which case can an F-test be used to compare two population means?

a. For one tail tests only. b. For two tail tests only. c. For either one or two tail tests. d. None of these choices.

7. When is the Tukey multiple comparison method used?

a. To test for normality. b. To test for differences in pairwise means. c. To test for equality of a group of population means. d. To test equal variances.

8. In one-way analysis of variance, within-treatments variation is measured by:

a. sum of squares for error. b. sum of squares for treatments. c. total sum of squares. d. standard deviation.

9. In one-way analysis of variance, if all the sample means are equal, then the:

a. total sum of squares is zero. b. sum of squares for treatments is zero. c. sum of squares for error is zero. d. sum of squares for error equals sum of squares for treatments.

Answer 1

1. In the one-way ANOVA where there are k treatments and n observations, the degrees of freedom for the F-statistic are equal to, respectively:

d. k − 1 and n − k.

2. In ANOVA, the F-test is the ratio of two sample variances. In the one-way ANOVA (completely randomized design), the variance used as a numerator of the ratio is:

a. mean square for between treatments.

3. The number of degrees of freedom for the denominator in one-way ANOVA test involving 4 population means with 15 observations sampled from each population is:

c. 56

4. For which of the following is not a required condition for ANOVA?

d. All of these choices are required conditions for ANOVA.

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