choices no. 5-7-9-10 The analysis of variance is a procedure that allows statist

Question

choices no. 5-7-9-10 The analysis of variance is a procedure that allows statisticians to compare two or more population: a. means. b. proportions. c. variances. d. standard deviations. The distribution of the test statistic for analysis of variance is the: a. normal distribution. b. Student t-distribution. c. F-distribution. d. None of these choices. 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. In the one-way ANOVA where k is the number of treatments and n is the number of observations in all samples, the degrees of freedom for treatments is given by: a. k-1 b. n-k c. n-1 d. n-k+1 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 treatments. b. mean square for error. c. total sum of squares. d. None of these choices. 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 equal: a. 24 b. 25 c. 29 d. 30

Explanation / Answer

5. Correct option:

a. means.

EXPLANATION: ANOVA is an analysis of variances in which there is only one independent variable It is used to determine the existence of differences among several population means.

7. Correct option:

d. k-1, n-k

EXPLANATION: F test statistic is found by dividing the between group variance by the within group variance. The degrees of freedom for the numerator are the degrees of freedom for the between group (k-1) and the degrees of freedom for the denominator are the degrees of freedom for the within group (n-k).

9. Correct option:

a. mean square for treatments.

EXPLANATION: F = MSC/MSE, where MSC is mean square for treatments and MSE is mean sum square for error.

10. Correct option:

d. 30

EXPLANATION; degrees of numerator = c-1=4. Degrees of denominator = n-c = 25. Adding these two, we get: n-1 = 4+25 = 29. So, n = 29 + 1 = 30.

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