Question

A scientist is testing certain sampling strategies to see which one is

best. She's gathered data from an entire population and calculates a
population mean μ (mu) = 14 and a population standard deviation
o (sigma) = 5. She draws five different samples from this population
using five different strategies and gets the following sample means and
standard deviations:
Sample 1:
(x-bar) = 16.9, s = 6
Sample 2:
(x-bar) = 14.5, s = 4.7
Sample 3:
(x-bar) = 10.5, s = 3.3
Sample 4:
(x-bar) = 17, s = 4.9
Sample 5: (x-bar) = 14.1, s= 8.4
Which sampling strategy does she conclude provides the best sample?

Answer 1

Step-by-step explanation: To determine which sampling strategy provides the best sample, we need to compare the sample means and standard deviations with the population mean and standard deviation.

Let's analyze each sample:

Sample 1:

Sample mean (x-bar) = 16.9

Sample standard deviation (s) = 6

Sample 2:

Sample mean (x-bar) = 14.5

Sample standard deviation (s) = 4.7

Sample 3:

Sample mean (x-bar) = 10.5

Sample standard deviation (s) = 3.3

Sample 4:

Sample mean (x-bar) = 17

Sample standard deviation (s) = 4.9

Sample 5:

Sample mean (x-bar) = 14.1

Sample standard deviation (s) = 8.4

Now, let's compare these values to the population mean (μ) and standard deviation (σ).

Population mean (μ) = 14

Population standard deviation (σ) = 5

By comparing the sample means to the population mean, we can see that Sample 1 (x-bar = 16.9) and Sample 4 (x-bar = 17) have higher means than the population mean, indicating that they might be closer to the true population mean.

However, when we consider the sample standard deviations, Sample 2 (s = 4.7) has the lowest standard deviation, indicating less variability within the sample.

Therefore, based on the given data, the sampling strategy with Sample 2 (x-bar = 14.5, s = 4.7) can be considered the best sample as it has a sample mean close to the population mean and a lower standard deviation compared to the other samples.