Question

Suppose we would like to compare spending based on income group: Low, Middle, and High. The Y-variable is "spending (dollars)" and the x-variable is "Income Group (low/middle/high)."

Suppose the p-value for this ANOVA is 0.00002

What do we conclude?

Question 8 options:

The average spending is the about the same for all three income groups.

Income group is not correlated with spending.

The high income group had the highest average spending.

The average spending for one of the income groups is different from the average spending of another income group.

The average spending is different for each income group; there is a group with the highest average spending, there is a group in the middle, and there is a group with the lowest average spending (i.e. there are no two groups whose average spending are about the same).

Answer 1

The researcher wants to compare spending based on income group: Low, Middle, and High. Here, the Y-variable is "spending (dollars)" and the x-variable is "Income Group (low/middle/high)."

It is given that the p-value for this ANOVA is 0.00002

Let (i = 1, 2, 3) represents average spending for all three income groups.

The null hypothesis (Ho) and the alternative hypothesis (Ha) can be framed as,

Ho: There is no difference between the average spending for all three income groups; that is, .

Ha: At least average spending for one of the income groups will differ; that is, .

Assume the significance level is 0.05.

To reach the conclusion compare p-value with the level of significance 0.05.

Since, the p-value 0.00002 is less than the significance level 0.05, so the decision is to reject the null hypothesis. Therefore, the researcher concludes that the average spending for one of the income groups is different from the average spending of another income group.

Hence, the correct statement is “The average spending for one of the income groups is different from the average spending of another income group”.