Question

At a home-and-garden show, randomly selected visitors were asked where they lived and where they normally shopped for their garden care products.

	garden shop	discount store	supermarket	TOTAL
Urban	11	20	15	46
Suburban	27	20	12	59
Rural	12	26	24	62
Total	50	66	51	167

[a] Fill in the table with the row percentages of each location category.

	Garden shop	discount store	supermarket
Urban
Suburban
Rural

[b] Write the null and alternate hypotheses for a test of independence on the data in the table.

[c] Calculate and report the P-value and record the expected values in the given table

P = ______

	Garden shop	discount store	supermarket
Urban
Suburban
Rural

[d] Is there evidence of association between where people live and where they shop for garden care products? Why or why not?

[e] Is there evidence that where people live influences where they shop for garden care products? Why or why not?

Answer 1

Ans:

a)

	Joint distribution
	garden shop	discount store	supermarket	Total
Urban	0.066	0.120	0.090	0.275
Suburban	0.162	0.120	0.072	0.353
Rural	0.072	0.156	0.144	0.371
Total	0.299	0.395	0.305	1.000

b)

H₀:There is no association  between where people live and where they shop for garden care products.

H_a:There is a association  between where people live and where they shop for garden care products

c)

	Observed(fo)
	garden shop	discount store	supermarket	Total
Urban	11	20	15	46
Suburban	27	20	12	59
Rural	12	26	24	62
Total	50	66	51	167
	Expected count(fe)
	garden shop	discount store	supermarket	Total
Urban	13.77	18.18	14.05	46
Suburban	17.66	23.32	18.02	59
Rural	18.56	24.50	18.93	62
Total	50	66	51	167
	Chi square=(fo-fe)^2/fe
	garden shop	discount store	supermarket	Total
Urban	0.558	0.182	0.065	0.805
Suburban	4.933	0.472	2.010	7.415
Rural	2.320	0.091	1.355	3.767
Total	7.812	0.746	3.430	11.987

Test statistic:

Chi square=11.987

df=(3-1)*(3-1)=4

p-value=CHIDIST(11.987,4)=0.0174

d)Assume significance level=0.05

As,p-value<0.05,we reject the null hypothesis.

There is sufficient evidence to conclude that there is a association between where people live and where they shop for garden care products