Question

Which of the following scenarios contain nonbiased samples?

Select all that apply:
a. Christine wants to estimate the mean grade point average of students at her school. She collects data by recording the grade point average of every 25th student on the list of students after a randomly selected first student.
b. Homer wants to estimate the ethnic background distribution of residents of his town. He collects data from 1000 randomly selected town residents by using a random number generator.
c. To estimate the mean height of students at her grade school, Tammy collects data by selecting a random group of students within her classroom.
d. To estimate the mean salary of professors at his university, Peter collects data by recording the salaries of all professors included in 12 randomly selected departments

Answer 1

From the scenarios provided, (a) and (b) could potentially contain nonbiased samples, depending on the initial selection in (a) and the demographic representation in (b).

Step-by-step explanation:

When discussing nonbiased samples, we are referring to samples that give each member of the population an equally likely chance of being chosen. In the scenarios provided:

• (a) This is a systematic sampling method, and it can be considered nonbiased if the first student was randomly selected and if there is no pattern in the list that might relate to GPA.
• (b) Using random number generator to select 1000 town residents ensures each member has an equal chance of being selected, making this a nonbiased sample.
• (c) Selecting a random group of students within a single classroom to estimate height may be biased due to lack of variability (e.g., all students in the same grade).
• (d) Collecting data by recording the salaries of professors in 12 randomly selected departments involves cluster sampling. It could be nonbiased if the departments were sufficiently diverse and represent the whole.

From the given scenarios, (a) and (b) appear to have nonbiased samples, provided (a)'s systematic approach started with a truly random initial selection and (b) truly represents the town's demographics.