Question

a national survey of 1200 adult citizens of a nation found that 16% dreaded valentines day. the margin of error for the survey was 1.5 percentage points with 85% confidence. explain what this means.
which statement or statements below correctly explain the survey results? select all that apply
□ a. there is 83.5% to 86.5% confidence that 16% of the adult citizens of the nation dreaded valentines day
□ b. there is 85% confidence that the proportion of the adult citizens of the nation that dreaded valentines day is between 0.145 and 0.175
□ c. there is a 85% probability that the proportion of the adult citizens of the nation that dreaded valentines day is between 0.825 and 0.855
□ d. there is 85% confidence that the proportion of the adult citizens of the nation that did not dread valentines day is between 0.825 and 0.855
□ e. there is 85% confidence that 16% of the adult citizens of the nation dreaded valentines day
□ f. in 85% of samples of adult citizens of the nation, the proportion that dreaded valentines day is between 0.145 and 0.175

Explanation:

• Confidence Interval Concept: A confidence interval gives a range of values within which the True population parameter is likely to lie. Here, the sample proportion \(p = 0.16\) and margin of error \(E=0.015\). The confidence interval is \(p - E
• Interpretation of Confidence Level: A \(85\%\) confidence level means that if we were to take many samples, about \(85\%\) of those samples would produce confidence intervals that contain the True population proportion.
• Option Analysis:
• Option A: Incorrect. The confidence is about the True proportion, not the sample proportion (\(16\%\) is the sample proportion).
• Option B: Incorrect. It should be about a range for the True proportion, not just stating the sample proportion with confidence.
• Option C: Incorrect. Confidence is not a probability for a single - sample interval. The True proportion is either in the interval or not.
• Option D: Incorrect. The values \(0.825\) and \(0.855\) are not related to the confidence interval for the proportion of people who dreaded Valentine's Day (\(0.145 - 0.175\)).
• Option E: Incorrect. The statement is about the non - dreading proportion, but the confidence interval was calculated for the dreading proportion.
• Option F: Correct. This is in line with the definition of a confidence interval. If we take multiple samples, about \(85\%\) of them will have a proportion of adults who dreaded Valentine's Day between \(0.145\) and \(0.175\).

Answer:

F. In \(85\%\) of samples of adult citizens of the nation, the proportion that dreaded Valentine's Day is between \(0.145\) and \(0.175\)