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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)The populationThe population is all voters in the district.The population is all the voters in the district who think the politician is doing a good job.    The population is a group of voters in the district.The population is a group of voters in the district who think the politician is doing a good job.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.Part (c)The parameterThe parameter is the number of people in the district.The parameter is the proportion of all voters in the district who think the politician is doing a good job.    The parameter is the proportion of a group of voters in the district who think the politician is doing a good job.The parameter is the number of registered voters in the district.Part (d)The statisticThe statistic is the number of registered voters in a group of people.The statistic is the number of people in the district.    The statistic is the proportion of a group of voters in the district who think the politician is doing a good job.The statistic is the number of voters in the district who think the politician is doing a good job.

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)The populationThe population is all voters in the district.The population is all the voters in the district who think the politician is doing a good job.    The population is a group of voters in the district.The population is a group of voters in the district who think the politician is doing a good job.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.Part (c)The parameterThe parameter is the number of people in the district.The parameter is the proportion of all voters in the district who think the politician is doing a good job.    The parameter is the proportion of a group of voters in the district who think the politician is doing a good job.The parameter is the number of registered voters in the district.Part (d)The statisticThe statistic is the number of registered voters in a group of people.The statistic is the number of people in the district.    The statistic is the proportion of a group of voters in the district who think the politician is doing a good job.The statistic is the number of voters in the district who think the politician is doing a good job.

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Solution

Part (a) The Population The population in this study refers to all the voters in the politician's district. This is the group that the politician is interested in understanding better.

Part (b) The Sample The sample in this study would be a subset of the population that is selected for analysis. For example, the politician might conduct a survey of 1,000 voters from his district to gauge their opinion on his performance. This group of 1,000 voters would be the sample.

Part (c) The Parameter The parameter in this study is the true proportion of all voters in the district who think the politician is doing a good job. This is the actual value that the politician is interested in, but it's often unknown and has to be estimated from the sample data.

Part (d) The Statistic The statistic in this study would be the observed proportion of voters in the sample who think the politician is doing a good job. This is used as an estimate of the parameter. For example, if 600 out of the 1,000 voters in the sample think the politician is doing a good job, the statistic would be 600/1000 = 0.6 or 60%.

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A political polling agency wants to take a random sample of registered voters and ask whether or not they will vote for a certain candidate. One plan is to select 400 voters, another plan is to select 1,600 voters.If the study were conducted repeatedly (selecting different samples of people each time), which one of the following would be true regarding the resulting sample proportions of "yes" responses? Different sample proportions would result each time, but for sample size 400 they would be centered (have their mean) at the true population proportion, whereas for sample size 1,600 they would not. Different sample proportions would result each time, but for either sample size, they would be centered (have their mean) at the true population proportion. Different sample proportions would result each time, but for sample size 1,600 they would be centered (have their mean) at the true population proportion, whereas for sample size 400 they would not. For either sample size, using the same size each time, as long as the samples are drawn with replacement, they would be centered (have a mean) at 0.

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