Question

Heather is a researcher interested in studying depression in high school students. They gather a sample from a local high school consisting of 17 male sophomores, 18 female sophomores, 17 male juniors, and 18 female juniors.

If they select one student at random, what is the likelihood that that student will be a male sophomore?

Answer 1

Stratified sampling is used in this scenario. The likelihood of selecting a male sophomore is 24.29%.

Step-by-step explanation:

The type of sampling used in this scenario is stratified sampling.

Stratified sampling is a sampling technique where the population is divided into homogeneous groups or strata, and a proportionate random sample is taken from each group. In this case, the groups are male sophomores, female sophomores, male juniors, and female juniors. One student is selected randomly from the sample, so there is an equal chance of selecting any of the students in the sample.

The probability of selecting a male sophomore can be calculated by dividing the number of male sophomores by the total number of students in the sample. There are 17 male sophomores out of a total of 17 male sophomores + 18 female sophomores + 17 male juniors + 18 female juniors = 70 students.

Therefore, the likelihood that the randomly selected student will be a male sophomore is:

(Number of male sophomores) / (Total number of students) = 17 / 70 = 0.2429 or 24.29%