Question

question 4
a management consultant was interested in whether workers who telecommute are as productive as those who work in the office. she randomly selected 60 workers who were in each of the following three groups: (1) full - time office workers, (2) part - time telecommuters, (3) full time telecommuters. after analyzing the data, the consultant noticed that the variation within groups was large relative to the variation between sample means.
which of the following is the most correct interpretation of this data?
a. the f statistic will be relatively large, so it is likely that the researcher can conclude that the population means may be equal.
b. the f statistic will be relatively large, so it is likely that the researcher can conclude that the population means are not all equal.
c. the f statistic will be relatively small, so it is likely that the researcher can conclude that the population means may be equal.
d. the f statistic will be relatively small, so it is likely that the researcher can conclude that the population means are not all equal.

Explanation:

The F - statistic in ANOVA is the ratio of between - group variance to within - group variance. When the variation within groups is large relative to the variation between sample means, the F - statistic will be small. A small F - statistic indicates that there is not enough evidence to reject the null hypothesis that the population means are equal.

Answer:

C. The F statistic will be relatively small, so it is likely that the researcher can conclude that the population means may be equal.