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:

Step1: Analyze first statement

The best estimate of population mean is often the mean of sample - means, and it usually lies between the least and greatest sample means. This is a valid concept in sampling.

Step2: Analyze second statement

The population mean is less likely to be the extreme (least or greatest) value among sample means as samples are random subsets. Extreme sample - means are outliers in the distribution of sample means.

Step3: Analyze third statement

If sample means have small variation, it indicates more consistency and they are better for predicting the population mean, not the opposite as stated.

Step4: Analyze fourth statement

Increasing the number of random samples generally gives a more accurate prediction of the population mean, not decreasing.

Step5: Analyze fifth statement

The range of any set of data (including sample means) is found by subtracting the least value from the greatest value. This is a correct way to calculate range.

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.