Question

west 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 seniors are randomly selected; 14 plan to go to a 4-year college.
○ 20 glee club members are randomly selected; 18 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 400 seniors at west 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

A random sample of the entire senior class (20 seniors randomly selected) is more likely to represent the entire population of seniors compared to samples from specific groups (honor roll, Glee Club).

Step2: Calculate the estimate

If in a sample of 20 seniors, 14 plan to go to a 4 - year college. The proportion of the sample planning to go to a 4 - year college is $\frac{14}{20}=0.7$.
If there are 400 seniors, the estimate is $400\times0.7 = 280$.

Answer:

(a) 20 seniors are randomly selected; 14 plan to go to a 4 - year college.
(b) 280