Question

A researcher is evaluating new cell phone designs. She suspects that individuals of different ages might have different preferences. She obtains a sample of 90 students from a nearby university and 60 older adults from the community center of a 55+ residential community. Each person had the opportunity to try out 3 phones and select their preference. Here are the observed frequencies:

1. What specific analysis should be used to determine whether design preference is independent of age?  

Observed Frequencies:

	Design 1	Design 2	Design 3
Student	20	56	14	90
Older Adult	32	10	18	60
	52	66	32

2.  Fill in the expected frequency table:

Expected Frequencies:

	Design 1	Design 2	Design 3
Student				90
Older Adult				60
	65	70	15

3.   Using a visual comparison only, is design preference independent of age?

Answer 1

1. Chi-Square analysis should be used to determine whether design preference is independent of age?  The Chi-Square test of independence is used to determine if there is a significant relationship between two nominal (categorical) variables.

2.

	OBSERVED	TABLE
Observed Frequencies:
	Design 1	Design 2	Design 3	TOATAL
Student	20	56	14	90
Older Adult	32	10	18	60
TOTAL	52	66	32	150
	E1=	RT*CT/GT =	90*52/150
			31.2
	E =	EXPECTED FREQ
	EXPECTED	TABLE
Expected Frequencies:
	Design 1	Design 2	Design 3	TOATAL
Student	31.2	39.6	19.2	90
Older Adult	20.8	26.4	12.8	60
TOTAL	52	66	32	150
3.
	CALCULATION TABLE
	O	E	O-E	(O-E)2/E
SD1	20	31.2	-11.2	4.02051282
OAD1	32	20.8	11.2	6.03076923
SD2	56	39.6	16.4	6.79191919
OAD2	10	26.4	-16.4	10.1878788
SD3	14	19.2	-5.2	1.40833333
OAD3	18	12.8	5.2	2.1125
SUM =	150	150	0	30.5519134
df=2			O=OBSERVED
level=0.05OR 5%			E= EXPECTED

H0: Design preference is independent of age  

H:1 Design preference is not independent of age  

= The Chi Square Statistics
= 30.5519
for ( =0.05 ) = the critical value is 5.99
Since the Chi Square Statistics > the critical value, Reject the null hypothesis.
so we conclude that Design preference is not independent of age