Question

una was asked to write about predicting population means by taking the means of samples. she recorded a list of some statements generated from her classmates. which statements are true? select three choices. the best prediction of the population mean is the value that falls between the least and greatest sample means. it is unlikely that the population mean will be the least or greatest mean from the samples. 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. a more accurate prediction of the population mean can be made by decreasing the number of random samples. to find the range of the sample means, subtract the least value from the greatest value.

Explanation:

1. For the first statement: The population mean is expected to lie within the range of sample means, so this is a valid best prediction range.
2. For the second statement: Sample means vary, and it is statistically unlikely the population mean matches the extreme (least/greatest) sample mean.
3. For the third statement: Small variation in sample means actually makes predictions more reliable, so this is false.
4. For the fourth statement: More random samples improve prediction accuracy, not fewer, so this is false.
5. For the fifth statement: Range is defined as greatest value minus least value, which applies to sample means.

Answer:

• The best prediction of the population mean is the value that falls between the least and greatest sample means.
• 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.