Question

Four different leadership styles used by Big-Six accountants were investigated. As part of a designed study, 15 accountants were randomly selected from each of the four leadership style groups (a total of 60 accountants). Each accountant was asked to rate the degree to which their subordinates performed substandard fieldwork on a 10-point scale—called the "substandard work scale". The objective is to compare the mean substandard work scales of the four leadership styles. The data on substandard work scales for all 60 observations were subjected to an analysis of variance.

Interpret the results of the ANOVA F test shown on the printout for a = 0.05.
a. At a = 05, there is insufficient evidence of differences among the substandard work scale means for the four leadership styles.
b. At a = .05, three is no evidence of differences among the substandard work scale means for the four leadership styles.
c. At a = .05, there is sufficient evidence of difference among at least two of the substandard work scale means for the four leadership styles.
d. None of the above.

Answer 1

At a = .05, there is sufficient evidence of difference among at least two of the substandard work scale means for the four leadership styles.

Step-by-step explanation:

The question is asking to interpret the results of an ANOVA F test conducted on the data collected from four different leadership styles used by Big-Six accountants. The objective was to compare the mean substandard work scales of the four leadership styles. The ANOVA F test is a statistical test used to determine whether there are any significant differences among the means of three or more groups.

According to the information provided, the level of significance is 0.05. The correct interpretation of the ANOVA F test results shown on the printout is: At a = .05, there is sufficient evidence of difference among at least two of the substandard work scale means for the four leadership styles.

Answer 2

c. At a = .05, there is sufficient evidence of difference among at least two of the substandard work scale means for the four leadership styles.

Step-by-step explanation:

From the given output, df(Between)=3

df (Between) =k-1, where, k denotes number of groups. Therefore, k-1=3, k=4.

Thus the null hypothesis is as follows:

H0:mu1=mu2=mu3=mu4 (there is no difference in substandard work scale means for four leadership styles)

H1: At least one mean scale is different from another.

Per rule, reject H0, if p value corresponding to F test statistic is less than given level of significance, alpha=0.05.

Here, F(3, 56)=6.056, p<0.05 (the p value is 0.0012). Therefore, reject H0, and conclude that at least one substandard work scale mean of a leadership is significantly different from a substandard work scale mean of another leadership.