Question

central 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?
∘ 25 honor roll students are randomly selected from the senior class; 18 plan to go to a 4-year college.
∘ 25 chess club members are randomly selected; 13 plan to go to a 4-year college.
∘ 25 seniors are randomly selected; 16 plan to go to a 4-year college.
(b) there are 450 seniors at central high. using your answer from part (a), estimate the number of seniors who plan to go to a 4-year college.

Explanation:

Part (a)

To best represent the entire population of seniors, the sample should be a random selection from all seniors, not a specific subgroup (like honor roll or chess club). The first option randomly selects 25 seniors from the whole senior class, making it the most representative.

Step1: Find the proportion from part (a)

The proportion of seniors planning to go to a 4 - year college in the sample is $\frac{16}{25}$.

Step2: Apply the proportion to the total number of seniors

To find the estimated number of seniors (total = 450) planning to go to a 4 - year college, we multiply the total number of seniors by the proportion: $450\times\frac{16}{25}$.
First, simplify $\frac{450}{25}=18$. Then, $18\times16 = 288$.

Answer:

25 seniors are randomly selected; 16 plan to go to a 4 - year college.

Part (b)