Sample data can be used to form an estimate about the population through several methods, but some are more commonly used than others. Here’s how the options you provided relate to this process:
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A range can be calculated to relate the sample to the population and solved to form an estimate.
- This could refer to creating confidence intervals, which involve estimating the range within which a population parameter (like the mean) is likely to fall based on sample data. This is a valid method of estimation.
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An expression can be written to relate the mean to the random group and solved to form an estimate.
- This could involve using the sample mean to estimate the population mean. This is also a valid approach, as the sample mean is commonly used as an unbiased estimator of the population mean.
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A proportion can be written to relate the sample to the mean and solved to form an estimate.
- This statement is a bit unclear, as it's more common to relate sample proportions to population proportions rather than means. However, you could use sample proportions to estimate population proportions effectively.
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A proportion can be written to relate the sample to the population and solved to form an estimate.
- This method is frequently used in statistics. For instance, if you're estimating a population proportion based on a sample proportion, you can use the sample data to make inferences about the population.
Overall, options 1, 2, and 4 are valid methods for using sample data to estimate population parameters. Option 1 relates to confidence intervals, option 2 focuses on estimating the mean, and option 4 focuses on proportions, which are standard practices in statistical estimation.
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