Question

At a particular college, $78\%$of all students are receiving some kind of financial aid. The school newspaper selects a random sample of $100$students and $72\%$of the respondents say they are receiving some sort of financial aid. Which of the following is true?

1. $78\%$is a population and $72\%$is a sample.
2. $72\%$is a population and $78\%$is a sample.
3. $78\%$is a parameter and $72\%$is a statistic.
4. $72\%$is a parameter and $78\%$is a statistic.
5. $72\%$is a parameter and $100$is a statistic.

Short answer

Option (c): $78\%$is a parameter and $72\%$is a statistic is correct option.

Step-by-step solution

Given Information

We are given that $78\%$of all students at a particular college get financial aid. From random sample of$100$students $72\%$respondents get financial statement.

We need to find out correct option from given options.

Explanation

All persons about whom we want to collect data are included in the population.
A sample is a subset of the population from which data is collected.
The sample in our question is the$100$ students in the random sample, whereas the population is defined as all students at a specific college.
A parameter is population descriptive measure, whereas a statistic is sample descriptive measure.
The $72\%$is based on a random sample of all students, hence$72\%$ is a statistic.
The $78\%$is based on all students at a specific college, hence it is based on the population, implying that $78\%$is a parameter.

From all above information we get conclusion that option c in correct option which states that $78\%$is a parameter and $72\%$is a statistic.