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 0.12. Each independently constructed a confidence interval based on the point​ estimate, but​ Jaime's interval has a lower bound of 0.078 and an upper bound of 0.193​, while​ Mariya's interval has a lower bound of 0.051 and an upper bound of 0.189. Which interval is​ wrong? Why?

Answer 1

Answer:

Jaime's. Interval not centered around the point estimate.

Step-by-step explanation:

When constructing a confidence interval based on a point estimate, the obtained point estimate must be the central value of the interval.

For Jaime's interval

Lower bound = 0.078

Upper Bound = 0.193

$Central = \frac{0.078+0.193}{2} =0.1355$

For Mariya's interval

Lower bound = 0.051

Upper Bound = 0.189

$Central = \frac{0.051+0.189}{2} =0.12$

For a point estimate of 0.12, only Mariya's interval is adequate since Jaime's is not centered around the point estimate.