Question

Phoenix Marketing identifies Los Angeles Naples and Washington DC as the three US cities with highest percentage of millionaires. Data consistent with the study show the following number of millionaires for sample of individuals from each of the three cities

Millionaires	Los Angeles	Naples	Washington DC	total
yes	40	30	30	100
No	270	360	370	1000
	310	390	400	1100

We intent to Test equality of population proportion of millionaires for these . Test Statistics (X²_calculation) is

Answer 1

Test statistic formula is given as below:

Chi square = ∑[(O – E)^2/E]

Where, O is observed frequencies and E is expected frequencies.

E = row total * column total / Grand total

Calculation tables for test statistic are given as below:

Observed Frequencies
	Column variable
Millionaires	Los Angeles	Naples	Washington DC	Total
Yes	40	30	30	100
No	270	360	370	1000
Total	310	390	400	1100

Expected Frequencies
	Column variable
Millionaires	Los Angeles	Naples	Washington DC	Total
Yes	28.18181818	35.4545455	36.36363636	100
No	281.8181818	354.545455	363.6363636	1000
Total	310	390	400	1100

Calculations
(O - E)
11.81818	-5.45455	-6.36364
-11.8182	5.454545	6.363636

(O - E)^2/E
4.956012	0.839161	1.113636
0.495601	0.083916	0.111364

Test Statistic = Chi square = ∑[(O – E)^2/E] = 7.599689826

χ2 statistic = 7.5997