Question

1. a mathematics professor decides to select a sample of 5 students from her class to put up the homework on the blackboard. her class size is 50 students. the professor wants to use the method of systematic sampling. if each student has been assigned a number from 1 to 50 and she randomly selects student number 8 as her first student, then determine the following: a) the ratio of the population size. b) identify the position of the students selected for the experiment.

Explanation:

Step1: Determine population and sample size

The class has 50 students (population size), and sample size is 5.

Step2: Calculate the ratio

The ratio of population size to sample size is $\frac{\text{Population Size}}{\text{Sample Size}}=\frac{50}{5}=10$.

Step3: Find positions of selected students

In systematic sampling with a first - selected number 8 and sampling interval $k = 10$, we add 10 successively to get 8, 8 + 10=18, 18+10 = 28, 28+10=38, 38 + 10=48.

Answer:

a) The population size is 50. The ratio of population size to sample size is $\frac{50}{5}=10$.
b) Since it is systematic sampling and the first - selected student number is 8, and the ratio (sampling interval) $k = 10$, the selected students' positions are 8, 18, 28, 38, 48.