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In a particular county, a sample of the population showed that
84% of the households lived in the same residence as they had the previous year. The estimate had a margin of error of
1.5% at the
90% confidence level. If the county has 50,000 households, which of the following best estimates the number of households that lived in the same residence as they had the previous year, at the
90% confidence level?
Choose 1 answer:
(A) 34,500 to 49,500 residents
(B) 37,500 to 50,000 residents
(C) 41,250 to 42,750 households
(D) 44,250 to 45,750 households

In a particular county, a sample of the population showed that $84 \%$ of the households lived in the same residence as they had the previous year. The estimate had a margin of error of $1.5 \%$ at the $90 \%$ confidence level. If the county has $50$ , $000$ households, which of the following best estimates the number of households that lived in the same residence as they had the previous year, at the $90 \%$ confidence level? $\newline$ Choose $1$ answer: $\newline$ (A) $34$ , $500$ to $49$ , $500$ residents $\newline$ (B) $37$ , $500$ to $50$ , $000$ residents $\newline$ (C) $41$ , $250$ to $42$ , $750$ households $\newline$ (D) $44$ , $250$ to $45$ , $750$ households

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Full solution

Q. In a particular county, a sample of the population showed that

84 \%

of the households lived in the same residence as they had the previous year. The estimate had a margin of error of

1.5 \%

at the

90 \%

confidence level. If the county has

50

,

000

households, which of the following best estimates the number of households that lived in the same residence as they had the previous year, at the

90 \%

confidence level?

\newline

Choose

1

answer:

\newline

(A)

34

,

500

to

49

,

500

residents

\newline

(B)

37

,

500

to

50

,

000

residents

\newline

(C)

41

,

250

to

42

,

750

households

\newline

(D)

44

,

250

to

45

,

750

households

Calculate point estimate: Calculate the point estimate of the number of households that lived in the same residence as they had the previous year. $\newline$ Point estimate = Percentage $*$ Total number of households $\newline$ = \(0. $84$ $*$ $50$ , $000$ \) $\newline$ = $42,000$
Calculate margin of error: Calculate the margin of error in terms of the number of households. $\newline$ Margin of error = Percentage margin of error $\times$ Total number of households $\newline$ $= 0.015 \times 50,000$ $\newline$ $= 750$
Determine lower bound: Determine the lower bound of the estimate at the $90$ % confidence level. $\newline$ Lower bound = Point estimate - Margin of error $\newline$ = $42,000 - 750$ $\newline$ = $41,250$
Determine upper bound: Determine the upper bound of the estimate at the $90$ % confidence level. $\newline$ Upper bound = Point estimate + Margin of error $\newline$ = $42,000 + 750$ $\newline$ = $42,750$
Identify correct answer: Identify the correct answer based on the calculated bounds. $\newline$ The correct answer is the range from the lower bound to the upper bound, which is $41,250$ to $42,750$ households.

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