Question

A poll was conducted on voter’s opinions on two candidates with margin of errors at 3.5%. Candidate A 38% Candidate Z 41% Undecided 21%

(a) Can we conclude that Candidate Z has a clear statistical lead over Candidate A? Briefly justify your answer.

(b)  Assuming 95% of confidence level, estimate the number of people participated in the poll. Round your answer to the nearest whole number.

Answer 1

Given Information:

A poll was conducted on voter’s opinions on two candidates A and B with margin of errors at 3.5%.

Defining the events:

: Proportion of voter’s opinions for candidate Z.

: Proportion of voter’s opinions for candidate A.

Since, the significance level is unknown so we take it as 5%.

The two tailed value of Z at 5% level of significance is 1.96.

The number of voters that voted for candidate Z is:

The number of voters that voted for candidate A is:

The pooled sample proportion is calculated as:

a) The null and the alternative hypothesis for difference in proportions is denoted by respectively and is given by:

The test is a right tailed test.

Under Null Hypothesis:

The calculated value of sample test statistic is given by:

The calculated value of test statistic is 0.58025.

Since, the calculated value of test statistic is less than tabulated value of test statistic, we conclude that the null hypothesis may be accepted that is there is no difference in the proportion of votes of candidate Z and candidate A.

we cannot conclude that Candidate Z has a clear statistical lead over Candidate A.

b)

The number of voters participated in the poll is given by:

Assuming 95% of confidence level, the number of people participated in the poll is 179.