Question

Tonya wanted to estimate the average amount of time that students at her school spend on Facebeek 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 mainly because it gave every possible sample of size 30 an equal chance to be selected. Therefore correct option is E

Step-by-step explanation:

Tonya's sample of students to determine Facebeek use is considered a simple random sample for a few reasons, but the primary one is that it involves selecting individuals purely by chance, giving all individuals an equal probability of being chosen. Let's look at the options to determine why Tonya's sample qualifies as a simple random sample:

• A) It doesn't involve strata or clusters - This is true; however, it is not the defining feature of a simple random sample.
• B) It was selected using a chance process - This is also true, but there's more.
• C) It is guaranteed to be representative of the population - This is NOT necessarily true. A simple random sample does not guarantee representativeness.
• D) It gave every individual the same chance to be selected - This is one of the defining characteristics of a simple random sample.
• E) It gave every possible sample of size 30 an equal chance to be selected - This is the most accurate definition of a simple random sample and the reason why Tonya's method of selecting a sample is correct.

Therefore, the best answer is E) because, in a simple random sample, every possible sample of the given size has the same chance of being selected.