The correct interpretation of a 99% confidence interval, such as (0.40, 0.52), is that we are 99% confident that the true population proportion lies within this interval.
The margin of error can be interpreted as half the width of the confidence interval. In this case, the margin of error is \((0.52 - 0.40) / 2 = 0.06\).
Given the options provided, none of them correctly interpret the margin of error. However, the closest correct interpretation regarding the sample and population proportions is:
- With 99% confidence, the sample proportion falls between 40% and 52%.
Note that this option should technically refer to the population proportion rather than the sample proportion, but it suggests an understanding of the interval itself.
The correct interpretation in statistical terms for the confidence interval would be: "With 99% confidence, the true population proportion lies between 0.40 and 0.52." However, since that option is not among the choices, if you have to select from the available options, you would choose:
With 99% confidence, the sample proportion falls between 40% and 52%.