central high wants to estimate the number of seniors who plan to go to a 4 - year college. answer the…

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; 17 plan to go to a 4 - year college. 25 glee club members are randomly selected; 15 plan to go to a 4 - year college. 25 seniors are randomly selected; 14 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. seniors

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; 17 plan to go to a 4 - year college. 25 glee club members are randomly selected; 15 plan to go to a 4 - year college. 25 seniors are randomly selected; 14 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. seniors

Answer

Explanation:

Step1: Identify representative sample

A representative sample should be randomly selected from the entire population of seniors. Selecting from honor - roll students or glee - club members is a non - representative sample as these are subsets with specific characteristics. Randomly selecting 25 seniors is the best representative sample.

Step2: Set up proportion

Let $x$ be the number of seniors who plan to go to a 4 - year college. We set up the proportion $\frac{14}{25}=\frac{x}{450}$ based on the ratio of seniors planning to go to a 4 - year college in the sample to the total number in the sample being equal to the ratio of the total number of such seniors in the population to the total population.

Step3: Solve proportion

Cross - multiply: $25x = 14\times450$. Then $25x=6300$. Divide both sides by 25: $x=\frac{6300}{25}=252$.

Answer:

(a) 25 seniors are randomly selected; 14 plan to go to a 4 - year college. (b) 252