A TV news reporter says that a proposed constitutional...

A TV news reporter says that a proposed constitutional amendment is likely to win approval in the upcoming election because a poll of 1505 likely voters indicated that $52 \%$ would vote in favor. The reporter goes on to say that the margin of error for this poll was $3 \%$. a) Explain why the poll is actually inconclusive. b) What confidence level did the pollsters use?

A TV news reporter says that a proposed constitutional amendment is likely to win approval in the upcoming election because a poll of 1505 likely voters indicated that $52 \%$ would vote in favor. The reporter goes on to say that the margin of error for this poll was $3 \%$.
a) Explain why the poll is actually inconclusive.
b) What confidence level did the pollsters use?

Key Concepts

Margin of Error

This is the maximum amount by which the estimated value from a sample might differ from the true population value. In polls, the margin of error reflects the uncertainty inherent in taking a sample rather than a complete census. Here, if the estimated approval is 52% with a 3% margin of error, the actual approval rate could reasonably be as low as 49% or as high as 55%, meaning the result is not definitively above the critical 50% threshold.

Confidence Interval

The confidence interval is a range calculated from the poll results that is likely to contain the true population parameter. It is constructed by adding and subtracting the margin of error from the sample percentage. When the confidence interval around the estimated value includes the threshold of interest (such as the 50% majority in this case), it indicates that the results are not statistically conclusive.

Confidence Level

The confidence level is the probability that the confidence interval produced by polling would contain the true population parameter if the same poll were repeated many times. In many cases, including typical political polling, a 95% confidence level is used. This implies that there is a 95% chance that the calculated interval, derived using a z-score of approximately 1.96, captures the true value. In this scenario, the margin of error provided suggests a 95% confidence level was likely employed by the pollsters.

Transcript

Please give Ace some feedback