Question

A national survey of 1000 adult citizens of a nation found that 25% dreaded Valentine's Day. The margin of error for the survey was 2.3 percentage points with 85% confidence. Explain what this means.Which statement below is the best explanation?A. There is 85% confidence that 25% of the adult citizens of the nation dreaded Valentine's Day.B. There is 85% confidence that the proportion of the adult citizens of the nation that dreaded Valentine's Day is between 0.227 and 0.273.C. There is 82.7% to 87.3% confidence that 25% of the adult citizens of the nation dreaded Vaentine's Day.D. In 85% of samples of adult citizens of the nation, the proportion that dreaded Valentine's Day is between 0.227 and 0.273.

Answer 1

Answer:

B. There is 85% confidence that the proportion of the adult citizens of the nation that dreaded Valentine's Day is between 0.227 and 0.273

Step-by-step explanation:

The confidence level means the confidence that we have that the true mean is in the interval calculated.

The margin of error represents the range of values below and above the sample statistic in a confidence interval. For example, if the sample statistic is 25% with a margin of error or 2.3%, the interval is between 25-2.3 = 22.7% and 25 + 2.3 = 27.3%.

So the correct answer is:

B. There is 85% confidence that the proportion of the adult citizens of the nation that dreaded Valentine's Day is between 0.227 and 0.273