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Francis surveyed a random sample of 70 students at Franklin High School about their favorite season. Of the students surveyed, 18 chose fall as their favorite season. There are 1816 students at Franklin High School.
Based on the data, what is the most reasonable estimate for the number of students at Franklin High School whose favorite season is fall?
Choose 1 answer:
(A) 257
(B) 467
(c) 515
(D) 1349

Francis surveyed a random sample of $70$ students at Franklin High School about their favorite season. Of the students surveyed, $18$ chose fall as their favorite season. There are $1816$ students at Franklin High School. $\newline$ Based on the data, what is the most reasonable estimate for the number of students at Franklin High School whose favorite season is fall? $\newline$ Choose $1$ answer: $\newline$ (A) $257$ $\newline$ (B) $467$ $\newline$ (C) $515$ $\newline$ (D) $\mathbf{1 3 4 9}$

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Interpret regression lines

Full solution

Q. Francis surveyed a random sample of

70

students at Franklin High School about their favorite season. Of the students surveyed,

18

chose fall as their favorite season. There are

1816

students at Franklin High School.

\newline

Based on the data, what is the most reasonable estimate for the number of students at Franklin High School whose favorite season is fall?

\newline

Choose

1

answer:

\newline

(A)

257

\newline

(B)

467

\newline

(C)

515

\newline

(D)

\mathbf{1 3 4 9}

Calculate Proportion: Calculate the proportion of students who chose fall as their favorite season from the survey. $\newline$ Proportion = Number who chose fall / Total surveyed $\newline$ Proportion = $\frac{18}{70}$ $\newline$ Proportion = $0.2571$
Estimate Number: Use the proportion to estimate the number of students in the entire school who prefer fall. $\newline$ Estimated number = Proportion $\times$ Total number of students at school $\newline$ Estimated number = $0.2571 \times 1816$ $\newline$ Estimated number = $466.6456$
Round to Nearest Whole: Since we can't have a fraction of a student, round to the nearest whole number. $\newline$ Estimated number $\approx 467$

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