Question

east 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 would best represent the entire population of seniors?
20 honor roll students are randomly selected from the senior class; 18 plan to go to a 4 - year college.
20 seniors are randomly selected; 15 plan to go to a 4 - year college.
20 glee club members are randomly selected; 17 plan to go to a 4 - year college.
(b) there are 500 seniors at east 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 - suited survey

A sample should be representative of the entire population. The honor roll students (\(20\) students) and the glee club members (\(20\) members) are subsets with specific characteristics. The \(20\) randomly selected seniors (\(20\) seniors are randomly selected from the senior class of \(18\) students) is more likely to be representative of all seniors.

Step2: Calculate the estimate

If in a sample of \(20\) randomly - selected seniors, \(15\) plan to go to a \(4 -\)year college. Let \(x\) be the number of seniors out of \(500\) who plan to go to a \(4 -\)year college.
We use the proportion \(\frac{\text{Number of students planning to go to 4 - year college in sample}}{\text{Sample size}}=\frac{\text{Number of students planning to go to 4 - year college in population}}{\text{Population size}}\)
The proportion is \(\frac{15}{20}=\frac{x}{500}\)
Cross - multiply: \(20x = 15\times500\)
\(20x=7500\)
Solve for \(x\): \(x=\frac{7500}{20}=375\)

Answer:

(a) \(20\) seniors are randomly selected from the senior class; \(18\) plan to go to go to a \(4 -\)year college.
(b) \(375\)