Final answer:
The statement that the standard error (SE) has a value between 0 and the original standard deviation (SD) of the data is true. SE is calculated as SD divided by the square root of the sample size, which makes it smaller than SD.
Step-by-step explanation:
The question seems to refer to the standard error (SE) and its relationship to the original standard deviation (SD) of a data set. When we consider the SE, it is indeed true that the SE has a value between 0 and the original SD of the data. This is because the SE is calculated as the standard deviation of the sample means, and it tends to be smaller than the original SD, especially as the sample size increases. This occurs due to the sampling distribution of the mean becoming more concentrated around the true population mean.
The SE is given by the formula SE = SD / √n, where SD is the standard deviation of the original data and n is the sample size. Since we are dividing by the square root of the sample size, the SE will naturally be smaller than the original SD as long as the sample size is greater than 1.