A politician is interested in the proportion of voters in his district who think he is doing a good job. Define the following in terms of the study. Give examples where appropriate.Part (a)Part (b)The sampleThe sample is all the voters in the district who think the politician is doing a good job.The sample is all voters in the district. The sample is a group of voters in the district who think the politician is doing a good job.The sample is a group of voters in the district.
Question
A politician is interested in the proportion of voters in his district who think he is doing a good job. Define the following in terms of the study. Give examples where appropriate.Part (a)Part (b)The sampleThe sample is all the voters in the district who think the politician is doing a good job.The sample is all voters in the district. The sample is a group of voters in the district who think the politician is doing a good job.The sample is a group of voters in the district.
Solution 1
Part (a) The Sample: In the context of this study, the sample refers to a subset of voters in the politician's district from whom data is collected. For example, this could be a group of 1000 voters selected at random from the district.
Part (b) The Sample: In this context, the sample could refer to all voters in the district. This would be a census, rather than a sample, and would include every individual voter's opinion on whether they think the politician is doing a good job. However, due to practical constraints, it's more likely that the sample refers to a smaller, representative group of voters from the district.
Solution 2
Part (a) The Population: The population in this study would be all the voters in the politician's district. This is because the politician is interested in the opinion of all voters in his district, not just a subset of them.
Part (b) The Sample: The sample in this study would be a subset of the population, i.e., a group of voters from the politician's district. This group would be selected to represent the population and their opinions would be used to estimate the proportion of all voters who think the politician is doing a good job. For example, the sample could be 1000 voters randomly selected from the district.
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