dentify the (a) sample and (b) population. Also determine whether the sample is likely to be representative of the population. a. A reporter for Newsweek stands on a street corner and asks 10 adults if they feel that the current president is doing a good job. b. Nielson Media Research surveys 5000 randomly selected households and finds that among the TV sets in use, 19% are tuned to 60 Minutes (based on data from USA Today). c. In a Gallup poll of 1059 randomly selected adults, 39% answered yes when asked Do you have a gun in your home? d. A graduate student at the University of Newport conducts a research project about how adult Americans communicate. She begins with a survey mailed to 500 of the adults that she knows. She asks them to mail back a response to this question: Do you prefer to use e-mail or snail mail (the US Postal Service)? She gets back 65 responses, with 42 of them indicating a preference for snail mail.
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a. The sample is the 10 adults that the Newsweek reporter asked about their opinion of the current president. Whether the sample is likely to be representative of the population depends on the specific characteristics of the adults on that street corner. If the street corner is in a diverse area and the reporter approaches a representative sample of adults, then the sample may be considered representative. However, if the street corner is in a specific neighborhood or if the adults approached are not a random selection, then the sample may not be representative.
b. The population is all households with TV sets in use. The sample is the 5000 randomly selected households that were surveyed. Since the households were randomly selected, the sample is likely to be representative of the population.
c. The population is all adults. The sample is the 1059 randomly selected adults surveyed in the Gallup poll. Since the adults were randomly selected, the sample is likely to be representative of the population.
d. The population is all adult Americans. The sample is the 500 adults that the graduate student mailed the survey to. Since the sample is not randomly selected and is based on the adults that the student knows, it is unlikely to be representative of the population.
a. The sample in this scenario is the 10 adults who were asked if they feel that the current president is doing a good job.
b. The population is all the households with TV sets in use. The sample is the 5000 randomly selected households surveyed by Nielson Media Research.
In both scenarios, it is likely that the samples are representative of the population. The reporter's sample of 10 adults may provide a general idea of public opinion, and Nielson Media Research's survey of 5000 randomly selected households allows for a larger and more diverse representation.
c. The population is all adults, and the sample is the 1059 randomly selected adults who were asked if they have a gun in their home. It may be reasonably representative of the population if the random selection was done properly.
d. The population is all adult Americans, and the sample is the 500 adults that the graduate student knows who were asked their preference for using e-mail or snail mail. This sample may not be representative of the population as the graduate student knows the participants, which introduces potential bias.
To identify the sample and population in each scenario and determine if the sample is likely to be representative, we need to consider the following:
a. Sample: The sample is the 10 adults that the reporter for Newsweek asked about their opinion on the current president's job.
Population: The population in this case would be all adults.
Representativeness: It is unlikely that the sample is representative of the population because it was not randomly selected and only includes individuals who happen to be on that specific street corner at that time. This may introduce bias and limit the generalizability of the findings.
b. Sample: The sample is the 5000 randomly selected households surveyed by Nielson Media Research.
Population: The population in this case would be all households.
Representativeness: The sample is likely to be representative of the population as it was randomly selected, which helps minimize bias and increase the likelihood of generalizing the findings to the entire population of households.
c. Sample: The sample is the 1059 randomly selected adults who participated in the Gallup poll.
Population: The population in this case would be all adults.
Representativeness: The sample is likely to be representative of the population as it was randomly selected. Random sampling helps ensure that there is an equal chance of every adult being included, increasing the likelihood of generalizing the findings to the entire population of adults.
d. Sample: The sample is the 65 adults who responded to the survey mailed by the graduate student at the University of Newport.
Population: The population in this case would be all adult Americans.
Representativeness: The sample is unlikely to be representative of the population as it is not randomly selected and only includes individuals known to the graduate student. This may introduce bias and limit the generalizability of the findings.
In summary, it is important to have a representative sample that is randomly selected to ensure that the findings can be generalized to the entire population.