Question

A professor wants to create an srs of 15 out of his 185 students. He labels his subjects as follows: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, . . . 185. Which statements accurately describe his labels? Check all that apply.

1) He labeled properly.
2) He did not label properly; he should have started at label 1.
3) He did not label properly; he should have stopped at label 15.
4) He did not label properly; he should have stopped at label 184.
5) He did not label properly; the labels do not contain the same number of digits.

Answer 1

The professor did not label his students properly for the simple random sample; he should have started at label 1, and all labels should contain the same number of digits to avoid bias in the sampling process.

Step-by-step explanation:

The question deals with the correctness of labels used by a professor who wants to create a simple random sample (SRS) of 15 students out of a total of 185. Understanding whether the labels are created properly is crucial for ensuring the validity of statistical sampling methods.

In this case, the statements that accurately describe the labelling are:

• 1) He did not label properly; he should have started at label 1.
• 5) He did not label properly; the labels do not contain the same number of digits.

Starting at label 0 can be problematic as zero does not always get equal treatment in random number generators and random sampling methods. Moreover, having labels with different lengths (number of digits) could introduce bias when using certain types of random number generators or when conducting a manual selection process.