A psychology program coordinator was interested in whether there was a difference in salary for the mental health counseling graduates of her master’s degree program based on whether they obtained employment in (1) a sole proprietor private practice, (2) a group private practice, (3) hospitals or (4) government agencies. After analyzing the data for 90 recent graduates, the consultant noticed that the variation within groups was small relative to the the variation between sample means.Which of the following is the most correct interpretation of this data? The F statistic will be relatively large, so it is likely that the researcher can conclude that the population means may be equal. The F statistic will be relatively large, so it is likely that the researcher can conclude that the population means are not all equal. The F statistic will be relatively small, so it is likely that the researcher can conclude that the population means may be equal. The F statistic will be relatively small, so it is likely that the researcher can conclude that the population means are not all equal.
Question
A psychology program coordinator was interested in whether there was a difference in salary for the mental health counseling graduates of her master’s degree program based on whether they obtained employment in (1) a sole proprietor private practice, (2) a group private practice, (3) hospitals or (4) government agencies. After analyzing the data for 90 recent graduates, the consultant noticed that the variation within groups was small relative to the the variation between sample means.Which of the following is the most correct interpretation of this data? The F statistic will be relatively large, so it is likely that the researcher can conclude that the population means may be equal. The F statistic will be relatively large, so it is likely that the researcher can conclude that the population means are not all equal. The F statistic will be relatively small, so it is likely that the researcher can conclude that the population means may be equal. The F statistic will be relatively small, so it is likely that the researcher can conclude that the population means are not all equal.
Solution 1
The F statistic will be relatively large, so it is likely that the researcher can conclude that the population means are not all equal.
This is because the F statistic in an ANOVA test is a ratio of the variance between group means to the variance within groups. If the variation within groups is small relative to the variation between sample means, this suggests that the groups are significantly different from each other, leading to a larger F statistic. A larger F statistic increases the likelihood of rejecting the null hypothesis that all population means are equal.
Solution 2
The F statistic will be relatively large, so it is likely that the researcher can conclude that the population means are not all equal. This is because the F statistic is a ratio of the variance between group means to the variance within groups. If the variation within groups is small relative to the variation between group means, this ratio will be large. A large F statistic typically indicates that at least one of the group means significantly differs from the others, suggesting that the population means are not all equal.
Similar Questions
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 the variation between sample means.Which of the following is the most correct interpretation of this data? The F statistic will be relatively large, so it is likely that the researcher can conclude that the population means may be equal. The F statistic will be relatively large, so it is likely that the researcher can conclude that the population means are not all equal. The F statistic will be relatively small, so it is likely that the researcher can conclude that the population means may be equal. The F statistic will be relatively small, so it is likely that the researcher can conclude that the population means are not all equal.
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