Question

A Census Bureau report on the income of Americans says that with 90% confidence the median income of all U.S. households in a recent year was$\backslash (57,005$with a margin of error of$\backslash )742$. Which of the following is the most appropriate conclusion?

a. $90\%$of all households had incomes in the interval$\backslash (57,005\pm \backslash )742$

b. We can be sure that the median income for all households in the country lies in the interval $\backslash (57,005\pm \backslash )742$

c. $90\%$ of the households in the sample interviewed by the Census Bureau had incomes in the interval $\backslash (57,005\pm \backslash )742$

d. The Census Bureau got the result$\backslash (57,005\pm \backslash )742$using a method that will capture the true median income$90\%$of the time when used repeatedly.

e. $90\%$ of all possible samples of this same size would result in a sample median that falls within $\backslash (742$of $\backslash )57,005$

Short answer

The required correct option is$\left(a\right)$

Step-by-step solution

Given information

Median income $=57,005$

Margin of error $\left(E\right)=742$

Confidence level$=90\%$

The objective is to draw the appropriate conclusion by selecting the correct option.

The confidence interval in which the population parameter is likely to fall provides the range.

The confidence interval is calculated as follows:

$CI=57005\pm 742$

In this case, there is a$90\%$chance that the median income of the households falls between $57005\pm 742$

Therefore, the correct option is$\left(a\right)$