Question

More shoppers do the majority of their grocery shopping on Saturday than any other day of the week. Determine whether there is a difference in the various age groups in the proportion of people who do the majority of their grocery shopping on Saturday.

A study reported that, of 200 shoppers under 35 years old, 56 did their major shopping on Saturday; of 200 shoppers between 35 and 54 years old, 80 did their major shopping on Saturday; and of 200 shoppers over 54 years old, 32 did their major shopping on Saturday, At the 0.05 level of significance, is there evidence of a difference among the age groups with respect to major grocery shopping day?

Answer 1

Null hypothesis:Ho: there is no  difference among the age groups with respect to major grocery shopping day

Alternate hypothesis:Ha: there is a difference among the age groups with respect to major grocery shopping day

degree of freedom(df) =(rows-1)*(columns-1)=		2
for 2 df and 0.05 level , critical value       χ2=		5.9915
Decision rule : reject Ho if value of test statistic X2>5.991
Applying chi square test :

Expected	Ei=row total*column total/grand total	<35	35-54	>54	Total
	did	70.00	28.00	70.00	168
	not did	130.00	52.00	130.00	312
	total	200	80	200	480
chi square    χ2	=(Oi-Ei)2/Ei	<35	35-54	>54	Total
	did	2.800	96.571	20.629	120.0000
	not did	1.508	52.000	11.108	64.6154
	total	4.3077	148.5714	31.7363	184.6154
test statistic X2 =		184.615

since test statistic falls in rejection region we reject null hypothesis

we have sufficient evidence to conclude that, there is a difference among the age groups with respect to major grocery shopping day