Decide whether or not the following samples are representative of the population

Question

Decide whether or not the following samples are representative of the population. If they are not representative, try to explain the reasons. To find the average GPA of all students in a university, use all honor students at the university as the sample. 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. To find the average annual income of all adults in the United States, sample U.S congressmen. Create a duster sample by considering each state as a stratum (group). By using simple random sampling, select states to be part of the duster. Then survey every U.S. congressman in the duster. 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. 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.
We need to find the average GPA of all students in a university. So, the population is all students in a university including honor and non-honor students.
So, the samples which are representatives of population are sample of both honor and nonhonor students.
So, all honor students at the university are not representatives of the whole population.

2.
Population is all types of cereals.
The samples will not be representative of population as it is considering only samples of cereals which are available in
supermarket, and not available by other means for e.g. online or home made cereals.

3.
Here population is all US adults including congressmen and non-congressmen.
The samples will not be representative of population as it is considering only samples of US congressman and not non-congressman adults.

4.
Here the population is people using public transportation to work.
The samples will not be representative of population as the person sitting in the park may not be using public transportation to work.
Also majority of person using public transportation to work may not be available sitting in the central park. Hence the survey conducted in Central park, may not produce a sample which is representative of the population.

5.
The population is hospitals in Massachusetts. We have used simple random sampling of 100 hospitals across the state. So the sample is the representative of the population.

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