Question

Two​ researchers, Jaime and​ Mariya, are each constructing confidence intervals for the proportion of a population who is​ left-handed. They find the point estimate is 0.14. Each independently constructed a confidence interval based on the point​ estimate, but​ Jaime's interval has a lower bound of 0.049 and an upper bound of 0.191​, while​ Mariya's interval has a lower bound of 0.079 and an upper bound of 0.201. Which interval is​ wrong? Why?

Answer 1

Jaime's wrong, becuase the distance(absolute value) from the point estimate to the lower bound is different than he distance from the upper bound to the point estimate.

Explanation:

The distance(absolute value) from the point estimate to the lower bound must be the same as the distance from the upper bound to the point estimate.

The point estimate is 0.14.

Jaime

Jaime's interval has a lower bound of 0.049 and an upper bound of 0.191

upper - point = 0.191 - 0.14 = 0.051

point - lower = 0.14 - 0.049 = 0.091

Jaime's wrong, becuase the distance(absolute value) from the point estimate to the lower bound is different than he distance from the upper bound to the point estimate.

Mariya

Just to check.

Mariya's interval has a lower bound of 0.079 and an upper bound of 0.201.

upper - point = 0.201 - 0.14 = 0.061

point - lower = 0.14 - 0.079 = 0.061

Mariya has the same distances, so it is correct.