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 probably 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: Understand sampling principles

For a sample to best represent the entire population, it should be randomly selected from the entire population. The honor roll students (\(20\) honor roll students selected from the senior class; \(18\) plan to go to a \(4 -\)year college) and glee club members (\(20\) glee club members are randomly selected; \(17\) plan to go to a \(4 -\)year college) are subsets of the senior population. Only the sample of \(20\) seniors randomly selected from all seniors (\(20\) seniors are randomly selected; \(15\) plan to go to a \(4 -\)year college) is randomly chosen from the whole senior population.

Step2: Calculate the estimate

The proportion of seniors in the sample who plan to go to a \(4 -\)year college is \(\frac{15}{20}\). There are \(N = 500\) seniors. Let \(x\) be the number of seniors who plan to go to a \(4 -\)year college. Using the proportion formula \(\frac{x}{N}=\frac{15}{20}\), we can solve for \(x\). Cross - multiply: \(20x=15\times500\), so \(x=\frac{15\times500}{20}\).

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Answer:

(a) The sample of \(20\) seniors randomly selected from all seniors. (b) \(375\)