Question

Problem 8 (15 marks) Five people have declared their intentions to run for a trustee seat in the next local election. Some political analysts claim that there is no clear preference among the voters. Hence, it is reported that each of the candidate would obtain 20% of the vote on his name A political poll is conducted during the campaign among 1,020 randomly sampled voters to determine if there is any clear preference among the voters. The responses are shown below. Candidate Responses 209 At a significance level a=0.05, can you infer that there is any clear preference among the voters? A B 269 с 229 D 159 E 154

Answer 1

Solution:

Here, we have to use chi square test for goodness of fit.

Null hypothesis: H₀: There are no any preferences among the voters.   

Alternative hypothesis: H_a: There are preferences among the voters.   

We are given level of significance = α = 0.05

We are given

Number of categories = N = 5

Degrees of freedom = df = N - 1 = 4

α = 0.05

Critical value = 9.48772904

(by using Chi square table or excel)

Test statistic formula is given as below:

Chi square = ∑[(O – E)^2/E]

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

Calculation tables for test statistic are given as below:

Candidate	O	E	(O - E)^2/E
A	209	204	0.12254902
B	269	204	20.7107843
C	229	204	3.06372549
D	159	204	9.92647059
E	154	204	12.254902
Total	1020	1020	46.0784314

Test Statistic = Chi square = ∑[(O – E)^2/E] = 46.0784314

χ² = 46.0784314

Critical value = 9.48772904

Test statistic value is greater than critical value.

So, we reject the null hypothesis

There is sufficient evidence to conclude that there is clear preference among the voters.