Question

Imagine that the average sentence length of a total of 500 prisoners is 4.2 years. The warden randomly sampled 20 prisoners and recorded their sentence. And then he repeated this procedure three more times. The means and standard errors are as follows. Which sample estimate shows the least sampling variability?

A) Sample one: mean=4.2, SE=5

B) Sample two: mean=6, SE=2

C) Sample three: mean= 3.7, SE=3

D) Sample four: mean= 4.6, SE=4

Answer 1

To determine which sample estimate has the least sampling variability, compare the standard errors (SE) of the four samples. The sample estimate with the least sampling variability will have the smallest standard error. The sample with the smallest standard error is Sample two, with a mean of 6 and a standard error of 2.

Step-by-step explanation:

To determine which sample estimate has the least sampling variability, we need to compare the standard errors (SE) of the four samples. The standard error measures the variability in sample means, indicating how close each sample mean is to the population mean. The sample estimate with the least sampling variability will have the smallest standard error.

Comparing the options:

1. Sample one: mean = 4.2, SE = 5
2. Sample two: mean = 6, SE = 2
3. Sample three: mean = 3.7, SE = 3
4. Sample four: mean = 4.6, SE = 4

Therefore, the sample estimate with the least sampling variability is Sample two with a mean of 6 and a standard error of 2.