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 σ (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: x̅ (x-bar) = 16.9, s=6
Sample 2: x̅ (x-bar) = 14.5, s=4.7
Sample 3: x̅ (x-bar) = 10.5, s=3.3
Sample 4: x̅ (x-bar) = 17, s=4.9
Sample 5: x̅ (x-bar) = 14.1, s=8.4

Answer 1

Which sampling strategy does she conclude provides the best sample

A. Sample 1
B. Sample 4
C. Sample 3
D. Sample 2
E. Sample 5

Answer 2

@Directrix

Answer 3

What is your thinking on this?

Answer 4

@hockeychick23

Answer 5

Sample 3 @Directrix

Answer 6

Why Sample 3? Is it the option with its sample mean and sample standard deviation closest to those of the population? @hockeychick23

Answer 7

I thought that because it had the smallest standard deviation it would be the correct answer.

Answer 8

but sample 5 is closest to 14

Answer 9

Compare both the mean and the standard deviation of the sample to those of the population.

The idea is that the sample should be as close in standard dev and mean to the population if the sample were properly drawn. (a bit of oversimplification there) but you get the idea.

Answer 10

Sample 5 has a bad standard deviation.

Answer 11

ok so sample 2 is close to both so would that be correct?

Answer 12

Correct, Sample 2.

Answer 13

ok thanks!

Answer 14

You are welcome.