Question

A market researcher is studying the spending habits of pople across age groups. The amount of money spent by each individual is classified by spending category (Dining out, Shopping, or Electronics) - Factor A, and generation (Gen-X, Gen-Y, Gen-Z, or Baby Boomers) - Factor B. An incomplete ANOVA table is shown below. At the 5% significance level, the conclusion of the hypothesis test for factor A is

Source of Variation	SS	df	MS	F	p-value	F crit
Rows (Factor B)				1.42	0.3398	2.92
Columns (Factor A)				3.15	0.0340	2.32
Error	455		16.25
Total	1,321	35

reject the null hypothesis; we cannot conclude the average amout spent differs by spending category

reject the null hypothesis; the average amout spent differs by spending category

do not reject the null hypothesis; we cannot conclude the average amout spent differs by spending category

do not reject the null hypothesis; the average amout spent differs by spending category

Answer 1

Solution:

Given:

Source of Variation	SS	df	MS	F	p-value	F crit
Rows (Factor B)				1.42	0.3398	2.92
Columns (Factor A)				3.15	0.0340	2.32
Error	455		16.25
Total	1,321	35

Factor A: spending category (Dining out, Shopping, or Electronics)

H0: the average amout spent does not differs by spending category.

Vs

H1: the average amout spent differs by spending category.

Decision Rule:
Reject null hypothesis H0, if P-value < 0.05 level of significance, otherwise we fail to reject H0

Since p-valuefor Factor A is 0.0340 < 0.05 level of significance, hence we reject the null hypothesis of no difference in the average amout spent by spending category.

Thus:

At the 5% significance level, the conclusion of the hypothesis test for factor A is:

Reject the null hypothesis; the average amout spent differs by spending category.