Chapter 5, Problem 5.81RE

(a)

To determine

To explain how would we choose an SRS of $250$ students.

Explanation of Solution

Given: A list of the $3500$ students at the school.

Simple random sampling uses a sample of size n in which every sample of size n has an equal chance of being chosen.

Randomly assign a unique number between $1\text{ and }3500$ to each student according to their rank in the provided list.

Randomly select $250$ unique integers between $1\text{ and }3500$ .

The $250$ students corresponding to the $250$ integers are then in the sample.

(b)

To determine

To explain how would we choose a systematic sample of $250$ students.

Explanation of Solution

Systematic random sampling is letting every kth individual be in the sample.

Randomly assign a unique number between $1\text{ and }3500$ to each student.

Since $\frac{3500}{250}=14$ , we randomly select an integer k between $1\text{ and }14$ .

The students in the sample are then $k,k+14,k+28,\mathrm{....},k+3486$ .

(c)

To determine

To explain how would we choose a stratified sample of $200$ bussed student and $50$ local students.

Explanation of Solution

Stratified random sampling draws simple random samples from independent subgroups.

BUSSED STUDENTS:

Randomly assign a unique number between $1\text{ and 2400}$ to each student according to their rank in the provided list.

Randomly select $200$ unique integers between $1\text{ and 2400}$ .

The $200$ bussed students corresponding to the $200$ integers are then in the sample.

LOCAL STUDENTS:

Randomly assign a unique number between $1\text{ and 1100}$ to each student according to their rank in the provided list.

Randomly select $50$ unique integers between $1\text{ and 1100}$ .

The $50$ local students corresponding to the $50$ integers are then in the sample.

To determine

(d)

To identify which of the three sampling method does we choose and why.

Answer to Problem 5.81RE

I would choose the stratified random sample.

Explanation of Solution

I would choose the stratified random sample in part (c), such that we were sure to include bussed and local students.