Question

a local politician claims that 55% of the community is in support of a proposed park expansion. the local newspaper conducts a study and obtains a 90% confidence interval of (0.4332, 0.6168). which statement best reflects the conclusion that can be made about the claim from the politician?

Answer 1

While the study's confidence interval includes the politician's claim of 55% support, it also encompasses other possibilities. Uncertainty remains, and the claim, though plausible, isn't definitively validated.

The Politician's Claim and the Confidence Interval: A nuanced picture

The situation you've described presents an interesting case where a politician's claim (55% support) falls within the range captured by a study's confidence interval (43.32% to 61.68%). However, simply stating that the claim is "consistent" with the interval wouldn't paint the whole picture. Here's a more nuanced breakdown:

The claim is plausible: Since 55% lies within the interval, the study's findings don't directly contradict the politician's assertion. The data suggests that the true level of support could indeed be around 55%.

But it's not the only possibility: The interval encompasses a range of values, not just 55%. This means there's also a chance that the actual support level falls somewhere else within that range, potentially higher or lower than the claim.

The confidence level matters: While the interval suggests plausibility, it's crucial to remember that it represents a 90% confidence level. This means that there's still a 10% chance that the true support level lies outside the interval, including outside the range supporting the claim.

Therefore, the most accurate conclusion would be to acknowledge the compatibility of the claim with the confidence interval while emphasizing the uncertainty inherent in such statistical estimates. A statement like this would capture the essence of the situation:

"The local newspaper's study found that between 43.32% and 61.68% of the community support the park expansion with 90% confidence. While this range includes the politician's claim of 55% support, it's important to remember that there is still a 10% chance the true level of support could fall outside this range."

This approach avoids misrepresenting the data or overstating the certainty surrounding the claim, providing a more balanced and informative perspective.