Question

A poll was conducted on voter’s opinions on two candidates with margin of errors at 3%.

Candidate B 35%

Candidate C 39%

Undecided 26%

(a) What is the confidence interval for the undecided?

(b) Which candidate has a lead? Is the lead statistically significant? Briefly justify your answer.

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

Answer 1

a)

Explanation:-

Confidence intervals :

Given the data is undecided 26%

Given sample proportion 'p' = 26% = 0.26

95% of confidence intervals are determined by

  

The confidence intervals for undecided (0.23 , 0.29)

b)

The Candidate 'C' has lead = 39%

Null hypothesis: P = 0.39

Alternative hypothesis : P 0.39

we can choose the sample proportion 'p'= 0.35 ( Candidate B)

we will use margin of error = 0.03

The test statistic

  

  

The z-score of 0.95 level of significance = 1.96

The tabulated value = 1.96

The calculated value 1.33 < 1.96 at 95% of level of significance

The null hypothesis is accepted.

Conclusion:-

The Candidate "C' is lead Satisfically significant.

  

  

c) Step(i):-

Given the data a poll was conducted on voter’s opinions on two candidates with margin of errors at 3%.

Candidate B 35%

   Candiate C 39%

The first sample proportion p1 = 35% = 0.35

q1 = 1-0.35 = 0.65

The second sample Proportion P2 = 39% = 0.39

q2 = 1-0.39 =0.61

Given the margin of error on two candidates = 3% =0.03

The margin of error for p1 - p2  is determined by

Step(ii)

Let us assume the sample size n = n1 =n2

The z-score of 0.95 level of significance = 1.96

On simplification, we get

Given margin of error (M.E) = 0.03

Squaring on both sides, we get

The sample size

Final Answer:-

The number of people participated in the poll = 1986