Final answer:
The question is about various sampling methods, specifically how to take a stratified sample, a systematic sample, and a cluster sample. For a stratified sample, divide the population into strata and take a proportional sample from each. Systematic sampling involves choosing elements at regular intervals, while cluster sampling involves selecting all elements within randomly chosen clusters.
Step-by-step explanation:
The question is related to different sampling methods used in statistics, which is a branch of mathematics. Given various sampling scenarios, the goal is to pick a sample that represents the population in a fair and unbiased manner. For example, taking a stratified sample involves dividing the population into subgroups (stratums) and then taking a proportional sample from each group. Similarly, a systematic sample is obtained by selecting elements from an ordered list at regular intervals. When we talk about taking samples without replacement, like from a group of employees, the chance of being selected changes as the drawing progresses because the population size decreases.
In the case of picking a stratified sample of restaurants by city or by entree cost, one would divide the total number of restaurants into groups based on the city or entree cost respectively. Then, 25 percent of each group is sampled, rounding to the nearest whole number to ensure a representative sample. For example, if there are 20 restaurants in a city, a stratified sample would include five restaurants from each stratum assuming uniform distribution.
Regarding the cluster sample, it involves random selection of entire groups or clusters from the population. When cities are used as clusters, you would randomly select two cities and then choose all the restaurants within those cities to include in the sample.