Question

Please assess whether preference for nuclear power is independent of country of origin at the 95% confidence level.

Select one: a. The chi square statistics is far greater than chi critical - we can reject the hypothesis that nuclear power preference is independent of country. b. The sample is too small to reject the null hypothesis. c. The chi square statistic is greater than chi critical, so we cannot reject the null. d. We can reject the null because the F statistic is greater than F critical.

Background Info:

F
Response	England	France	Italy	Spain	Germany	US
Strongly Favor	141	161	298	133	128	204	1065
Favor more than oppose	348	366	309	222	272	326	1843
Oppose more than favor	381	334	219	311	322	316	1883
Strongly oppose	217	215	219	443	389	174	1657
	1087	1076	1045	1109	1111	1020	6448
E
Response	England	France	Italy	Spain	Germany	US
Strongly Favor
Favor more than oppose
Oppose more than favor
Strongly oppose
Error^2/e:
Response	England	France	Italy	Spain	Germany	US
Strongly Favor
Favor more than oppose
Oppose more than favor
Strongly oppose

Answer 1

a. The chi square statistics is far greater than chi critical - we can reject the hypothesis that nuclear power preference is independent of country.

Solution:

Here, we have to use chi square test for independence of two categorical variables.

Null hypothesis: H₀: The preference for nuclear power is independent of country of origin.

Alternative hypothesis: H_a: The preference for nuclear power is not independent of country of origin.

We are given confidence level = 95% = 0.95, so level of significance = α = 1 – 0.95 = 0.05

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

We are given

Number of rows = r = 4

Number of columns = c = 6

Degrees of freedom = df = (r – 1)*(c – 1) = 3*5 = 15

α = 0.05

Critical value = 24.99579

(by using Chi square table or excel)

Calculation tables for test statistic are given as below:

F	Observed (O)
Response	England	France	Italy	Spain	Germany	US	Total
Strongly Favor	141	161	298	133	128	204	1065
Favor more than oppose	348	366	309	222	272	326	1843
Oppose more than favor	381	334	219	311	322	316	1883
Strongly oppose	217	215	219	443	389	174	1657
Total	1087	1076	1045	1109	1111	1020	6448
E	Expected (E)
Response	England	France	Italy	Spain	Germany	US
Strongly Favor	179.5371	177.7202	172.6	183.1708	183.5011	168.4708
Favor more than oppose	310.6918	307.5478	298.6872	316.98	317.5516	291.5416
Oppose more than favor	317.435	314.2227	305.1698	323.8596	324.4437	297.8691
Strongly oppose	279.3361	276.5093	268.543	284.9896	285.5036	262.1185
Error^2/e:	(O - E)^2/E
Response	England	France	Italy	Spain	Germany	US
Strongly Favor	8.27186	1.573067	91.10747	13.74185	16.78666	7.492816
Favor more than oppose	4.479997	11.10938	0.356072	28.45984	6.53422	4.072777
Oppose more than favor	12.72861	1.24479	24.33149	0.510624	0.018406	1.103603
Strongly oppose	13.91079	13.6827	9.140082	87.6077	37.51796	29.6235

Chi square = ∑[(O – E)^2/E] = 425.4063

P-value = 0.00

(By using Chi square table or excel)

P-value < α = 0.05

So, we reject the null hypothesis

There is sufficient evidence to conclude that the preference for nuclear power is not independent of country of origin.