Question

identify the sampling techniques used, and discuss potential sources of bias (if any). explain. every twentieth person entering a cafeteria is asked to choose his or her favorite meal from a list of five different meals that includes a description of each. a. cluster sampling is used, because the population is divided into groups, several groups are selected, and every person in those groups is contacted. b. stratified sampling is used, because the population is divided into groups, and random samples are taken from each group. c. systematic sampling is used, because every twentieth person is selected. d. simple random sampling is used, because every sample of a given size has an equal chance of being selected. e. convenience sampling is used, because the researchers contact the easiest people to reach. what potential sources of bias are present, if any? select all that apply. a. if there is a regular pattern to the people entering the cafeteria, the sample may not be representative. b. people who do not enter the cafeteria are not sampled. c. the wording of the question may direct respondents towards a particular meal. d. there are no potential sources of bias.

Explanation:

1. Sampling technique: Systematic sampling involves selecting every $k^{th}$ element from a population. Here, every twentieth person is selected, which fits the definition of systematic sampling.
2. Sources of bias:

• A: If there is a pattern in the people entering (e.g., certain groups enter at specific times), the sample may not represent the entire population of interest.
• B: Only people entering the cafeteria are sampled, excluding those who don't, which can lead to bias as the non - cafeteria - entering population is not represented.
• C: The way the question is worded and the description of meals could influence respondents' choices.

Answer:

1. Sampling technique: C. Systematic sampling is used, because every twentieth person is selected.
2. Potential sources of bias: A. If there is a regular pattern to the people entering the cafeteria, the sample may not be representative; B. People who do not enter the cafeteria are not sampled; C. The wording of the question may direct respondents towards a particular meal.