Question

a small western town is split in two, divided in half by a river that runs through the middle of the town. the local chamber of commerce wants to survey residents about a proposal to shut down the fish hatchery on the outskirts of town. the chamber of commerce will select one side of town and survey every 5th house. then the chamber will go to the other side of town and survey every 5th house. which of the following is the best description of the type of sample the chamber will select?
a) simple random sample
b) convenience sample
c) systematic random sample
d) stratified random sample
e) cluster sample

1. a large high school hosts a “freshmen orientation” day before school starts to introduce new students to the school. during freshmen orientation, students are placed into groups of eight freshmen and two seniors who act as leaders. groups do activities throughout the day to get to know each other. a random sample of 3 groups was taken and each individual in the group – freshman and seniors – were surveyed. which of the following statements about the sample of 30 is true?

a) it is a systematic random sample because the students were systematically divided into groups of 8 freshmen.
b) it is a stratified random sample because all students were selected from some of the groups.
c) it is a stratified random sample because some of the students were selected from each group.
d) it is a cluster sample because all of the students were surveyed from the randomly selected groups.
e) it is a cluster sample because some of the students were selected from each group.

Explanation:

1. In the first - case, since the chamber of commerce selects every 5th house to survey, this is a systematic random sample. In systematic random sampling, elements are selected at regular intervals from an ordered population.
2. In the second - case, groups are formed (clusters) of freshmen and seniors, and then all the individuals within 3 randomly selected groups are surveyed. This is a cluster sample. A cluster sample involves dividing the population into groups (clusters) and then randomly selecting some of these clusters and including all the elements within the selected clusters in the sample.

Answer:

1. C. Systematic random sample
2. D. It is a cluster sample because all of the students were surveyed from the randomly selected groups.