Question

10 message If we took an SRS of 1700 people from California (population 34 million) and an SRS of 1000 people from Detroit (population 1 million) which sampling distribution would have the smaller standard deviation?

Answer 1

California

Explanation:

The standard deviation of a sampling distribution also called standard error is obtained using the relation :

Standard Error = σ / sqrt(n)

Where n = sample size ; σ = population standard deviation

From the relation above, the higher the sample size of the sampling distribution, the lower the standard error because n is the denominator.

Therefore, California with a sample size of 1700 will have a lower standard error value Than Detroit with a sample size of 1000