The following data are the semester tuition charges ($000) for a
sample of private colleges in various regions of the United States.
At the .05 significance level, can we conclude there is a difference
in the mean tuition rates for the various regions?
Northeast Southeast West
($000) ($000) ($000)
10 8 7
11 9 8
12 10 6
10 8 7
12 6
(a) State the null and the alternate hypotheses.
(b) What is the decision rule?
(c) Develop an ANOVA table.
(d) What is the value of the test statistic?
(e) What is your decision regarding the null hypothesis?
(a) Null hypothesis (H0): The mean tuition rates for the various regions are equal.
Alternate hypothesis (Ha): There is a difference in the mean tuition rates for the various regions.
(b) Decision rule:
Reject the null hypothesis if the calculated F-statistic is greater than the critical F-value for a significance level of 0.05.
(c) ANOVA table:
Source of Variation | SS | df | MS | F
Between groups | 19.67 | 2 | 9.84 |
Within groups | 26.57 | 13 | 2.04 |
Total | 46.24 | 15 |
(d) The F-statistic is calculated by dividing the mean square between groups by the mean square within groups: 9.84/2.04 = 4.82
(e) Compare the F-statistic (4.82) to the critical F-value for a significance level of 0.05 with degrees of freedom 2 and 13. If the calculated F-statistic is greater than the critical F-value, reject the null hypothesis. If it is less than the critical F-value, fail to reject the null hypothesis.