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Based on random samples of river heights, oceanographers estimate that 4,800 cubic kilometers
(km^(3)) of freshwater is discharged into the Arctic Ocean annually. The estimate has a margin of error of
240km^(3) at the
90% confidence level. Which of the following is the most reasonable claim about the volume of freshwater discharged annually into the Arctic Ocean?
Choose 1 answer:
A It is between 4,800 and
5,040km^(3).
(B) It is between 4,560 and
5,040km^(3).
(C) It is between 240 and
4,800km^(3).
(D) It is between 240 and
4,320km^(3).

Based on random samples of river heights, oceanographers estimate that $4$ , $800$ cubic kilometers $\left(\mathrm{km}^{3}\right)$ of freshwater is discharged into the Arctic Ocean annually. The estimate has a margin of error of $240 \mathrm{~km}^{3}$ at the $90 \%$ confidence level. Which of the following is the most reasonable claim about the volume of freshwater discharged annually into the Arctic Ocean? $\newline$ Choose $1$ answer: $\newline$ A) It is between $4$ , $800$ and $5,040 \mathrm{~km}^{3}$ . $\newline$ B) It is between $4$ , $560$ and $5,040 \mathrm{~km}^{3}$ . $\newline$ (C) It is between $240$ and $4,800 \mathrm{~km}^{3}$ . $\newline$ (D) It is between $240$ and $4,320 \mathrm{~km}^{3}$ .

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Interpret confidence intervals for population means

Full solution

Q. Based on random samples of river heights, oceanographers estimate that

4

,

800

cubic kilometers

\left(\mathrm{km}^{3}\right)

of freshwater is discharged into the Arctic Ocean annually. The estimate has a margin of error of

240 \mathrm{~km}^{3}

at the

90 \%

confidence level. Which of the following is the most reasonable claim about the volume of freshwater discharged annually into the Arctic Ocean?

\newline

Choose

1

answer:

\newline

A) It is between

4

,

800

and

5,040 \mathrm{~km}^{3}

.

\newline

B) It is between

4

,

560

and

5,040 \mathrm{~km}^{3}

.

\newline

(C) It is between

240

and

4,800 \mathrm{~km}^{3}

.

\newline

(D) It is between

240

and

4,320 \mathrm{~km}^{3}

.

Calculate lower limit: Calculate the lower limit of the confidence interval. $\newline$ Lower limit = Estimate - Margin of error $\newline$ = $4,800 \, \text{km}^3 - 240 \, \text{km}^3$ $\newline$ = $4,560 \, \text{km}^3$
Calculate upper limit: Calculate the upper limit of the confidence interval. $\newline$ Upper limit = Estimate + Margin of error $\newline$ = $4,800 \, \text{km}^3 + 240 \, \text{km}^3$ $\newline$ = $5,040 \, \text{km}^3$
Determine volume range: Determine the range of the estimated volume of freshwater. The range is between the lower limit and the upper limit. So, the volume of freshwater is estimated to be between $4,560\,\text{km}^3$ and $5,040\,\text{km}^3$ .
Match with options: Match the calculated range with the given options. $\newline$ The calculated range is between $4,560\,\text{km}^3$ and $5,040\,\text{km}^3$ , which corresponds to option $(B)$ .

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