Question

CALCULATE THE x² Statistics and use it to...

A survey asked participants whether they shop online and recorded their age to explore a potential association between the two variables. The ages were then grouped into "above 30 years old' and '30 years or younger'. The data are summarised in the following table, together with row percentages. Age group Above 30 years old 30 years or younger Total Frequently 52 (26%) 47 (39%) 99 (31%) Shop online Rarely Never Total 94 (47%) 54 (27%) 200 (100%) 52 (43%) 21 (18%) 120 (100%) 146 (46%) 75 (23%) 320 (100%)

Answer 1

Solve using Excel:

A B C D E F H 1 ACTUAL Never Total N 94 54 Frequently Rarely 3 Above 30 52 4 30 or younger 47 5 Total 99 52 21 200 120 320 146 75 6 FORMULA FOR EXPECTED VALUE =(B$5*$E3)/$E$5 =(C$5*$E3)/$E$5 =(D$5*$E3)/$E$5 =(B$5*$E4)/$E$5 =(C$5*$E4)/$E$5 =(D$5*$E4)/$E$5 7 EXPECTED 8 Frequently Rarely Never 9 Above 30 61.881 91.25 46.88 10 30 or younger 37.13 54.75 28.13 11 12 CHI-SQUARE 13 Frequently Rarely Never 14 Above 30 1.58 0.08 1.08 15 30 or younger 2.63 0.14 1.81 16 17 Test statistic 7.31 ESUM(B14:D15) 18 Critical value 5.99 ECHISQ.INV.RT(0.05,2) FORMULA FOR CHI-SQUARE =(B3-B9)^2/B9 =(03-09)^2/09 =(D3-09)^2/09 =(B4-B10)^2/B10 =(C4-C10)^2/C10 =(D4-D10)^2/010

	ACTUAL
	Frequently	Rarely	Never	Total
Above 30	52	94	54	200
30 or younger	47	52	21	120
Total	99	146	75	320
	EXPECTED
	Frequently	Rarely	Never		FORMULA FOR EXPECTED VALUE
Above 30	61.88	91.25	46.88		=(B$5*$E3)/$E$5	=(C$5*$E3)/$E$5	=(D$5*$E3)/$E$5
30 or younger	37.13	54.75	28.13		=(B$5*$E4)/$E$5	=(C$5*$E4)/$E$5	=(D$5*$E4)/$E$5
	CHI-SQUARE
	Frequently	Rarely	Never		FORMULA FOR CHI-SQUARE
Above 30	1.58	0.08	1.08		=(B3-B9)^2/B9	=(C3-C9)^2/C9	=(D3-D9)^2/D9
30 or younger	2.63	0.14	1.81		=(B4-B10)^2/B10	=(C4-C10)^2/C10	=(D4-D10)^2/D10
Test statistic	7.31	=SUM(B14:D15)
Critical value	5.99	=CHISQ.INV.RT(0.05,2)

H₀: Participant's age is independent of whether they shop online

H₁: Participant's age is not independent of whether they shop online

Test statistic = 7.31

Degrees of freedom: df = (rows-1)*(columns-1) = (2-1)*(3-1) =2, Level of significance = 0.05

Critical value (Using Excel function CHISQ.INV.RT(probability, df)) = CHISQ.INV.RT(0.05,2) = 5.99

Since test statistic is greater than critical value, we reject the null hypothesis.

Conclusion: Participant's age is not independent of whether they shop online.