Question

A human resource manager wants to see if there is a difference in the proportion of minority applicants who get the job and the proportion of Caucasian applicants who get the job. After reviewing the records, she came up with the following confidence interval for the difference between the proportions: [ − 0.23 , − 0.15 ] . The sample mean difference was -0.19. The error bound is defined by: Right Endpoint - Sample Mean Difference Find the error bound.

Answer 1

Error Bound = 0.04

Explanation:

Whenever we want to estimate parameter from a subset (or sample) of the population, we need to considerate that your estimation won't be a 100% precise, in other words, the process will have a random component that prevents us from always making the exact decision.

With that in mind, the objective of a confidence interval is to give us a better insight of where we expect to find the "true" value of the parameter with a certain degree of certainty.

The estivamative of the true difference between proportions was -0.19 and the confidence interval was [-0.23 ; -0.15].

The question also defines the error bound, as the right endpoint of the confidence interval minus the sample mean difference, so it's pretty straight foward:

Error Bound =
`-0.15 -(-0.19) = -0.15 + 0.19 = 0.04`

The interpretation of this would be that we expect that the estimative for the difference of proportions would deviate from the "true" difference about
`\pm 0.04` or 4%.