Question

At Central High School, 28% of the students are Freshmen, 26% are Sophomores, 24% are Juniors, and 22% are Seniors. The student manager of the school newspaper would like to conduct a survey to estimate the proportion of each class that plans to attend the upcoming Football game. She suggests surveying a random sample of 100 students, but specifically by selecting random samples of 28 Freshmen, 26 Sophomores, 24 Juniors, and 22 Seniors. Which of the following is a true statement about this sampling procedure?

(A) This is a simple random sample because students of every class have an equal chance of being selected.
(B) This is a cluster random sample because there are 4 groups of students that are to be selected.
(C) This is a convenience sample because only 100 students are surveyed, which is a manageable size.
(D) This is a stratified random sample because a separate random sample is selected from each class
(E) Yes, because the difference between the sample proportion and the population proportion is 0.04, which is less than 0.05.

Answer 1

(D) This is a stratified random sample because a separate random sample is selected from each class

Explanation:

A sample of size n is defined to be a stratified random sample if it is selected from a population which has been divided into a number of non overlapping groups or sub populations called strata, such that part of the sample is drawn at random from each stratum.

It is to be emphasized that good stratification requires that each of these strata should be internally homogeneous but externally should differ from one another.

The advantage of stratified sampling is low cost , greater accuracy and better coverage.

If we analyze the given scenario a sample is selected from each strata depicting its corresponding percentage in the population. It is internally homogeneous but externally different.