Q.1 - The Practice of Statistics for AP

Question

A study of voting chose $663$ registered voters at random shortly after an election. Of these,  $72\%$said they had voted in the election. Election records show that only$56\%$ of registered voters voted in the election. Which of the following statements is true about the boldface numbers?

 (a)$72\%$ is a sample; $56\%$ is a population.

(b) $72\%$ and$56\%$ are both statistics.

(c)$72\%$ is a statistic and $56\%$ is a parameter.

(d) $72\%$ is a parameter and $56\%$ is a statistic.

(e) $72\%$ and$56\%$ are both parameters.

Step-by-Step Solution

Answer

Correct option is option (c) $72\%$ is a statistic and $56\%$ is a parameter

Step 1: Given information

Given in the question that, A study of voting chose $663$ registered voters at random shortly after an election. Of these,$72\%$said they had voted in the election. Election records show that only $56\%$ of registered voters voted in the election

Step 2: Explanation

Number of registered voters $=663$

Percent of voters who said they voted in the election $=72\%$

Percent of registered voters who voted in the election$=56\%$

Know that a descriptive measure for a population is a parameter and a descriptive measure for a sample is a statistic.

Here, since the proportion$72\%$ is based on the study of randomly selected numbers of voters that is, $663$ ; so $72\%$ is a statistic.

Also, the proportion $56\%$ is based on all registered voters. This means the $52\%$ is a parameter.

Thus, $72\%$ is a statistic and $56\%$is a parameter.

Hence, the correct answer is (c).