Question

In exercises 4-6, a survey reported that 235 of the 500 voters in a sample voted for candidate A and the rest voted for candidate B?

4. What percent of the voters in the sample voted for candidate A? What percent of the voters in the sample voted for candidate B?

5. What is the margin sampling error? Round your answer to the nearest tenth of a percent.

6. For each candidate, give an interval that is likely to contain the exact percent of all voters who voted for the candidate.

7. For #6, can you determine which candidate won? Explain.

Answer 1

4.

Total voters = 500

Number of voters that voted for candidate A = 235

Number of voters that voted for candidate B = 500 - 235 = 265

Percent of voters that voted for candidate A

= 235

500

× 100%

= 23500

500

= 47%

Percent of voters that voted for candidate B

= 265

500

× 100%

= 26500

500

= 53%

5.

Margin sample error = % of candidate B - 5 of candidate A

= 53% - 47%

= -/+ 6%

Margin sample error = + 6.0% or - 6.0%

6.

Candidate A interval

= 47 ± 0.5

= 46.5% or 47.5%

Candidate B interval

= 53±0.5

= 52.5% or 53.5%

7.

Candidate with the highest percentage win.

Therefore, candidate B won