Question

central high wants to estimate the number of seniors who plan to go to a 4-year college. answer the followi
(a) which of the following surveys probably would best represent the entire population of seniors?
50 glee club members are randomly selected; 44 plan to go to a 4-year college.
50 seniors are randomly selected; 29 plan to go to a 4-year college.
50 honor roll students are randomly selected from the senior class; 34 plan to go to a 4-year college.
(b) there are 650 seniors at central 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 - representative sample

A random sample of the entire senior class (50 seniors randomly selected) is more likely to represent the entire population of seniors compared to a sample from a specific subgroup like honor roll students or Glee Club members.

Step2: Calculate the estimate for part (b)

The proportion of seniors in the sample who plan to go to a 4 - year college is \(\frac{29}{50}\).
To estimate the number of seniors in the whole class (\(N = 650\)) who plan to go to a 4 - year college, we use the formula \(\text{Estimate}=N\times\text{Proportion}\).
So, \(\text{Estimate}=650\times\frac{29}{50}\).
First, simplify \(\frac{650}{50}=13\).
Then, \(13\times29=(10 + 3)\times29=10\times29+3\times29=290+87 = 377\).

Answer:

(a) 50 seniors are randomly selected; 29 plan to go to a 4 - year college.
(b) 377