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In a poll of 1,578 randomly selected American adults,
44.8% of the respondents said that airlines should allow in-flight calls on airplanes. The poll reported a margin of error of
2.5% at a
95% confidence level. Which of the following is most likely to be equal to the percentage of all American adults who would say that airlines should allow in-flight calls?
Choose 1 answer:
(A)
40%
(B)
43%
(C)
48%
(D)
95%

In a poll of $1$ , $578$ randomly selected American adults, $44.8 \%$ of the respondents said that airlines should allow in-flight calls on airplanes. The poll reported a margin of error of $2.5 \%$ at a $95 \%$ confidence level. Which of the following is most likely to be equal to the percentage of all American adults who would say that airlines should allow in-flight calls? $\newline$ Choose $1$ answer: $\newline$ (A) $40 \%$ $\newline$ (B) $43 \%$ $\newline$ (C) $48 \%$ $\newline$ (D) $95 \%$

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Full solution

Q. In a poll of

1

,

578

randomly selected American adults,

44.8 \%

of the respondents said that airlines should allow in-flight calls on airplanes. The poll reported a margin of error of

2.5 \%

at a

95 \%

confidence level. Which of the following is most likely to be equal to the percentage of all American adults who would say that airlines should allow in-flight calls?

\newline

Choose

1

answer:

\newline

(A)

40 \%

\newline

(B)

43 \%

\newline

(C)

48 \%

\newline

(D)

95 \%

Given Data: We are given that $44.8\%$ of the respondents in the poll said that airlines should allow in-flight calls. We are also given a margin of error of $2.5\%$ at a $95\%$ confidence level. This means that the true percentage of all American adults who believe airlines should allow in-flight calls is likely within $2.5\%$ above or below the reported percentage.
Calculate Range: To find the range within which the true percentage lies, we subtract the margin of error from the reported percentage to find the lower bound and add the margin of error to the reported percentage to find the upper bound. $\newline$ Lower bound = $44.8\% - 2.5\% = 42.3\%$ $\newline$ Upper bound = $44.8\% + 2.5\% = 47.3\%$
Comparison with Options: Now we compare the calculated range with the given options to determine which is most likely to be equal to the percentage of all American adults who would say that airlines should allow in-flight calls. $\newline$ (A) $40\%$ is below the lower bound. $\newline$ (B) $43\%$ is within the range. $\newline$ (C) $48\%$ is above the upper bound. $\newline$ (D) $95\%$ is not relevant to the margin of error and is far outside the range.
Most Likely Percentage: The most likely percentage is the one that falls within the calculated range. Option (B) $43\%$ is the only option that falls within the range of $42.3\%$ to $47.3\%$ .

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