Let's analyze the statements one by one to determine which ones are true:
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The best prediction of the population mean is the value that falls between the least and greatest sample means.
- False. The best prediction of the population mean is generally the mean of the sample means, rather than just a value between the least and greatest sample means.
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It is unlikely that the population mean will be the least or greatest mean from the samples.
- True. The population mean is more likely to fall within the range of the sample means rather than being the extreme values (least or greatest).
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If the means of different samples are close in number, or have small variation, then they cannot be used to make predictions for the actual population.
- False. If the means of different samples are close in number and have small variation, it actually indicates that these sample means provide a reliable estimate for the population mean.
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A more accurate prediction of the population mean can be made by decreasing the number of random samples.
- False. Generally, increasing the number of random samples improves the accuracy of the prediction for the population mean due to the reduction of sampling error.
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To find the range of the sample means, subtract the least value from the greatest value.
- True. This statement is accurate; the range is calculated as the difference between the maximum and minimum values.
Based on the analysis, the three true statements are:
- It is unlikely that the population mean will be the least or greatest mean from the samples.
- To find the range of the sample means, subtract the least value from the greatest value.