Decide whether or not the following samples are representative of the population
ID: 3297752 • Letter: D
Question
Decide whether or not the following samples are representative of the population. If they are not representative, try to explain the reasons. Please inlcuding which type of sampling in each scenario (Methods include: Simple Random, Convenience, Systematic, Cluster, and Stratified, Multistage Sampling (in which some of the methods above are combined in stages).
1. To find the average GPA of all students in a university, use all honor students at the university as the sample.
2. To find out the most popular cereal among children under the age of ten in America, stand outside a large supermarket near your home for three hours and speak to every twentieth child under age ten who enters the supermarket.
3. To find the average annual income of all adults in the United States, sample U.S. congressmen. Create a cluster sample by considering each state as a stratum (group). By using simple random sampling, select states to be part of the cluster. Then survey every U.S. congressman in the cluster.
4. To determine the proportion of people taking public transportation to work, survey 20 people in New York City. Conduct the survey by sitting in Central Park on a bench and interviewing every person who sits next to you.
5. To determine the average cost of a two-day stay in a hospital in Massachusetts, survey 100 hospitals across the state using simple random sampling.
Explanation / Answer
1. To find the average GPA of all students in a university, use all honor students at the university as the sample.
Answer : NO, because sample must be representative of entire sample so selecting all honor students is not coorect sampling.
2. To find out the most popular cereal among children under the age of ten in America, stand outside a large supermarket near your home for three hours and speak to every twentieth child under age ten who enters the supermarket.
Answer : NO That is good method as the selection process is random. Here we select 20th child so it is random so we can call it a random sampling. But, it is not also a perfect sample as it is limited to nearby supermarket only, not representating other geographical area so No, the sample is not representative of entire US chld population eating preferences.
3. To find the average annual income of all adults in the United States, sample U.S. congressmen. Create a cluster sample by considering each state as a stratum (group). By using simple random sampling, select states to be part of the cluster. Then survey every U.S. congressman in the cluster
Answer: YES, that's a perfect example of cluster sampling.
4. To determine the proportion of people taking public transportation to work, survey 20 people in New York City. Conduct the survey by sitting in Central Park on a bench and interviewing every person who sits next to you.
Answer : YES, sample size is pretty small but the process used here is totally random so we can say the sample is a representation of the population.
5.To determine the average cost of a two-day stay in a hospital in Massachusetts, survey 100 hospitals across the state using simple random sampling.
Answer : No, surveying 100 hospitals will not serve any real purpose here. We have to find random sample from among the people.
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