Question

The contingency table to the right shows counts of the types of gasoline bought during the week and during weekends. ​(a) Find the value of​ chi-squared and​ Cramer's V for this table. ​(b) Interpret these values. What do these tell you about the association in the​ table?

Weekday Weekend Total   Premium 127127 124124 251251   Plus 100100 203203 303303   Regular 487487 128128 615615   Total 714714 455455 11691169

​(a)

chiχsquared2equals=nothing

​(Round to two decimal places as​ needed.)

Vequals=nothing

​(Round to two decimal places as​ needed.)

​(b) Interpret the values from part​ (a). What do they indicate about the​ association?

Since

▼

Upper VV

chi squaredχ2

is

▼

somewhat large

rather small

large

​, there is

▼

strong

weak

moderate

association between the two variables.

chart with given information

Premium - Weekday 127 Weekend 124 Total 251

Plus- Weekday 100 Weekend 203 Total 303

Regular-Weekday 487 Weekend 128 Total 615

Total-Weekday 714 Weekend 455 Total 1169

Since V or X to the second is somewhat large rather small or large there is strong weak or moderate association between the two variables.

Answer 1

a)

Applying chi square test of independence:

Observed		weekday	weekend	Total
	Premium	127	124	251
	Plus	100	203	303
	regular	487	128	615
	total	714	455	1169
Expected	Ei=row total*column total/grand total	weekday	weekend	Total
	Premium	153.305	97.695	251.00
	Plus	185.066	117.934	303.00
	regular	375.629	239.371	615.00
	total	714.00	455.00	1169.00
chi square    χ2	=(Oi-Ei)2/Ei	weekday	weekend	Total
	Premium	4.514	7.083	11.5967
	Plus	39.101	61.358	100.4587
	regular	33.021	51.817	84.8380
	total	76.6352	120.2583	196.893
test statistic X2 =		196.89

Cramer V=φc=√(X2/(n*(k-1)))=sqrt(196.89/(1169*(2-1)) =

0.41 (here k =minimum of number of rows and columns)

  b)

Since V is somewhat large   there is strong association between the two variables.