Question

In yet another hypothetical earthly country, at a particular point in that country’s history, and with regard to the results of a simple random sample, n=1200, of the country’s eligible voters, we observe ideological differences among those voters on the question of whether emissions of carbon dioxide (from power-generating plants and other sources) should be regarded and regulated as polluting emissions.   We have the following data, observable in our survey results:

	Conservative	Reformist	Undefined	Totals
Should	125	270	170	565
Should not	275	90	165	530
Don't know	25	40	40	105
Totals	425	400	375	1200

Compute the following under the null hypothesis of independence between a voter’s political ideology and that voter’s perspective on characterization/regulation of carbon dioxide emissions.

(i)

How many conservatives would we expect to express the point of view that CO₂ emissions should not be regarded and regulated as polluting emissions?

(ii)

How many reformists would we expect to express the point of view that CO₂ emissions should be regarded and regulated as polluting emissions?

(iii)

How many eligible voters with no defined ideology would we expect to express not knowing the answer to this question?

Among the answer choices that follow, CHOOSE THE BEST COMBINATIONS OF THE OPTIONS GIVEN IN (i) AND (ii) AND (iii).

Group of answer choices

a.

(i)

200

(ii)

177

(iii)

35

b.

(i)

199

(ii)

189

(iii)

105

c.

(i)

189

(ii)

177

(iii)

166

d.

(i)

201

(ii)

188

(iii)

40

e.

None of the above answer sets is correct.

Answer 1

(i)

How many conservatives would we expect to express the point of view that CO₂ emissions should not be regarded and regulated as polluting emissions?

Row total : CO₂ emissions should not be regarded and regulated as polluting emissions = 530

Column total : conservatives = 425

Grand total = 1200

Number conservatives  expected to express the point of view that CO₂ emissions should not be regarded and regulated as polluting emissions =

Row Total x column Total Grand x Total 530 x 425 -= 187.7083 1200

(ii)

How many reformists would we expect to express the point of view that CO₂ emissions should be regarded and regulated as polluting emissions

Row total : CO₂ emissions should be regarded and regulated as polluting emissions = 565

Column total : reformist = 400

Grand total = 1200

Number of reformists expected to express the point of view that CO₂ emissions should be regarded and regulated as polluting emissions

Row Total x column Total Grand x Total 565 x 400 -= 188.3333 1200

(iii)

How many eligible voters with no defined ideology would we expect to express not knowing the answer to this question?

Row total :  not knowing the answer to this question: Don't Know = 105

Column total :no defined ideology:undefined = 375

Grand total = 1200

Number of eligible voters with no defined ideology expected to express not knowing the answer to this question

Row Total x column Total Grand x Total 105 X 375 -= 32.8125 1200

Among the answer choices that follow, CHOOSE THE BEST COMBINATIONS OF THE OPTIONS GIVEN IN (i) AND (ii) AND (iii).

Ans :

e.

None of the above answer sets is correct.

Expected values for all the cells

E: Expected Count/Frequency	Conservative	Reformists	undefined
Should	(565*425) / 1200	(565*400) / 1200	(565*375) / 1200
Should not	(530*425) / 1200	(530*400) / 1200	(530*375) / 1200
Did not know	(105*425) / 1200	(105*400) / 1200	(105*375) / 1200

E: Expected Count/Frequency	Conservative	Reformists	undefined
Should	200.1041667	188.3333333(ii)	176.5625
Should not	187.7083333(i)	176.6666667	165.625
Did not know	37.1875	35	32.8125(iii)