Question

A researcher wanted to know if a particular brand was preferred by different age groups. The researcher observed the data below. Is there a relationship between age and brand?

	Brand A	Brand B	Brand C
Under 30	120	130	110
30 – 50	77	127	140
50 and older	84	100	98

1. Which test are you using?
2. What are your H0 (null hypothesis) and Ha (alternative hypothesis)?
3. Calculate your statistic.
4. What decision does this inform you to make and why? (You may use the critical value in the chart or the calculated p-value, but you must indicate what you are doing.)
5. Write a one to two sentence conclusion that correctly responds to the question.

Please use only  Chi-Squared test

Answer 1

a)

We have to use here chi-square test.

b)

The null and alternative hypothesis is:

H0: There is no relationship between age and brand.

H1: There is a relationship between age and brand.

Level of significance = 0.05

c)

Test statistic is

O: Observed frequency
E: Expected frequency.
E = ( Row total*Column total) / Grand total

	Brand A	Brand B	Brand C	Total
Under 30	120	130	110	360
30-50	77	127	140	344
50 and older	84	100	98	282
Total	281	357	348	986

O	E	(O-E)	(O-E)^2	(O-E)^2/E
120	102.5963	17.40365	302.8871	2.952221
130	130.3448	-0.34483	0.118906	0.000912
110	127.0588	-17.0588	291.0035	2.290305
77	98.03651	-21.0365	442.5348	4.51398
127	124.5517	2.448276	5.994055	0.048125
140	121.4118	18.58824	345.5225	2.845873
84	80.36714	3.63286	13.19767	0.164217
100	102.1034	-2.10345	4.424495	0.043333
98	99.52941	-1.52941	2.3391	0.023502
			Total	12.882

d)

Degrees of freedom = ( Number of rows - 1 ) * ( Number of column - 1) = ( 3 - 1) * (3 - 1) = 2 * 2 = 4

Critical value = 9.488

( From chi-square table)

e)

Test statistic > Critical value we reject null hypothesis.

Conclusion:

There is a relationship between age and brand.