i. For the population means, the alternate hypothesis used in the analysis of variance test states thatµ₁=µ₂=µ₃. ii. For an ANOVA test, rejection of the null hypothesis does not identify which populations differ significantly. iii. If the computed value of F is 4.01 and the critical value is 2.67, we would conclude that all the population means are equal. A) (i), (ii), and (iii) are all correct statements. B) (ii) is a correct statement but not (i) or (iii). C) (iii) is a correct statement but not (i) or (ii). D) (ii) and (iii) are correct statements but not (i). E) (i), (ii), and (iii) are all false statements.

Question

Quizplus · Accepted Answer

Statement (ii) is correct since rejection of the null hypothesis only indicates that there is at least one population mean that is different from the others, but it does not identify which one(s) specifically. Statement (iii) is incorrect because if the computed value of F is greater than the critical value, it indicates that at least one population mean differs significantly from the others. Therefore, we would reject the null hypothesis and conclude that at least one population mean is different from the others. Statement (i) is also incorrect since the alternative hypothesis for ANOVA tests typically assumes that at least one population mean is different from the others, but it does not specify which one(s) specifically.

I for the Population Means, the Alternate Hypothesis Used in the Analysis