Question

A group conducted a poll of 2025 likely voters just prior to an election. The results of the survey indicated that candidate A would receive 47​% of the popular vote and candidate B would receive 46​% of the popular vote. The margin of error was reported to be 2​%. The group reported that the race was too close to call. Use the concept of a confidence interval to explain what this means. What does it mean to say the race was too close to​ call?

Answer 1

Check Explanation

Explanation:

Confidence Interval for the population proportion is basically an interval of range of values where the true population proportion can be found with a certain level of confidence.

Mathematically,

Confidence Interval = (Sample proportion) ± (Margin of error)

The population proportion can take on any value within the confidence interval obtained.

So, for each candidate, we can calculate the confidence interval for the population proportion of popular votes they would each receive.

For candidate A,

Sample Proportion = 47%

Margin of Error = 2%

Confidence Interval = (47%) ± (2%)

Confidence interval = (45%, 49%)

For candidate B,

Sample Proportion = 46%

Margin of Error = 2%

Confidence Interval = (46%) ± (2%)

Confidence interval = (44%, 48%)

The true proportion of popular votes for the two candidates will lie between

Confidence Interval for candidate A

(45%, 49%)

Confidence Interval for candidate B

(44%, 48%)

So, the true proportion of popular votes for candidate A can take on any value from 45% to 49%, and that for candidate B can take on values from 44% to 48%.

Because, A could have 45% and B have 48% or A could have 47% and B too have 47%.

The clear winner cannot be determined from this confidence interval obtained from the survey, it really is too close to call!

Hope this Helps!!!