Question

Tonya wanted to estimate the average amount of time that students at her school spend on Facebee each day. She gets an alphabetical roster of students in the school from the registrar’s office and numbers the students from 1 to 1137. Then Tonya uses a random number generator to pick 30 distinct labels from 1 to 1137. She surveys those 30 students about their Facebee use.

Tonya’s sample is a simple random sample because
A)it doesn’t involve strata or clusters.
B)It was selected using a chance process.
C)it is guaranteed to be representative of the population.
D)it gave every individual the same chance to be selected.
E)it gave every possible sample of size 30 an equal chance to be selected.

Answer 1

Tonya's sampling method is a simple random sample as it gave every individual the same chance to be selected, which is option D).

Step-by-step explanation:

Tonya’s sample is a simple random sample because it is D) it gave every individual the same chance to be selected. Simple random sampling is a method where each member of the population has an equal chance of being included in the sample. This method was used by Tonya since all students were numbered and a random number generator selected 30 distinct numbers corresponding to students. Thus, every student from the roster had an equal chance of being selected, which is a key characteristic of simple random sampling.

Answer choice E) is also a characteristic of simple random sampling, however, it pertains to every possible sample of size 30 having an equal chance to be selected, not the individuals themselves. Likewise, C) cannot be guaranteed in any sampling method. Therefore, the answer that suits the description of Tonya's method the most is D).