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Answer:
Error Bound = 0.04
Step-by-step 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 =
The interpretation of this would be that we expect that the estimative for the difference of proportions would deviate from the "true" difference about or 4%.
For this case we have the following system of equations:
Equating both equations we have:
We must find the solutions, for this we factor. We look for two numbers that, when multiplied, result in 4 and when added, result in 5. These numbers are 4 and 1:
Then, the factorized equation is of the form:
Thus, the solutions are:
We look for solutions for the variable "y":
Thus, the system solutions are given by:
ANswer: