Question

northside high wants to estimate the number of seniors who plan to go to a 4 - year college. answer the following.
(a) which of the following surveys probably would best represent the entire population of seniors?
20 chess club members are randomly selected; 18 plan to go to a 4 - year college.
20 seniors are randomly selected; 15 plan to go to a 4 - year college.
20 honor roll students are randomly selected from the senior class; 16 plan to go to a 4 - year college.
(b) there are 500 seniors at northside high. using your answer from part (a), estimate the number of seniors who plan to go to a 4 - year college.
□ seniors

Explanation:

Step1: Determine the best survey

To best represent the entire population of seniors, the sample should be randomly selected from all seniors. Chess Club members and honor - roll students are subsets of seniors with specific characteristics (e.g., interest in chess or high academic performance), which may not be representative of all seniors. Selecting 20 seniors randomly is more representative.

Step2: Calculate the estimate

If 15 out of 20 randomly - selected seniors plan to go to a 4 - year college, the proportion is $\frac{15}{20}=\frac{3}{4}$.
If there are \(N = 500\) seniors, the estimate \(x\) is found by setting up a proportion \(\frac{x}{500}=\frac{15}{20}\).
Cross - multiply: \(20x=15\times500\).
So, \(x=\frac{15\times500}{20}\).
Simplify: \(x=\frac{7500}{20}=375\).

Answer:

(a) 20 seniors are randomly selected; 15 plan to go to a 4 - year college.
(b) 375 seniors