Question

Teenagers make up a large percentage of the market for clothing. Below are data on running shoe ownership in four world regions (excluding China). At α = .01, does this sample show that running shoe ownership depends on world region?

Running Shoe Ownership in World Regions
Owned By	U.S.	Europe	Asia	Latin America	Row Total
Teens	80	89	69	65	303
Adults	20	11	31	35	97
Col Total	100	100	100	100	400

http://lectures.mhhe.com/connect/0077837304/Excel/Ch15/Running.xlsx

(a)	The hypothesis for the given issue is H0: Age Group and World Region are independent.

Yes No

(b)	Calculate the chi-square test statistic, degrees of freedom, and the p-value. (Round your test statistic value to 2 decimal places and the p-value to 4 decimal places.)

Test statistic
d.f.
p-value

(c)	Find the critical value for chi-Square. Refer to the chi-square http://lectures.mhhe.com/connect/0077837304/Images/appendixe.jpg table. (Round your answer to 2 decimal places.) Critical value    (d) We reject the null hypothesis. Yes No

Answer 1

Here we need to test if sample show that running shoe ownership depends on world region.

a) The hypothesis for the given issue is H0: Age Group and World Regionare independent.

The correct option is : Yes

The expected count :

So expected count is given by

	U.S.	Europe	Asia	Latin America
Teens	75.75	75.75	75.75	75.75
Adults	24.25	24.25	24.25	24.25

b)

Observed Frequency(O)	Expected Frequency (E)
80	75.75	0.2384
20	24.25	0.7448
89	75.75	2.3177
11	24.25	7.2397
69	75.25	0.5191
31	24.25	1.8789
65	75.25	1.3962
35	24.25	4.7655
		19.1003

Hence the test statistic is

= 19.10

Here number of rows = 2 , number of columns = 4

df = ( r-1 )( c -1 ) = ( 2 -1 )(4-1) = 1 * 3 = 3

p value = p ( < 19.10 )

Use excel function "=chisq.dist(x, df , cummulative ) " " =chisq.dist.rt(19.10,3,1)"

So p value = 0.0003.

c) Here α = 0.01, df = 3

Use exccel function "=chisq.inv(probability,df ) " "=chisq.inv.rt(0.01,3)"

So we get Critical value = 11.34

d. Here calculated value of > Critical value of .

Also p value < ( 0.01 )

Hence we reject null hypothesis