Question

When taking a random sample from a very large population, how does the standard error of the mean change when a. the sample size is increased from 100 to 1,600? b. the sample size is decreased from 300 to 150? c. the sample size is multiplied by 4? ​

Answer 1

a. the sample size is increased from 100 to 1,600?

Explanation:

The theorem states that if large random samples of n observations are drawn from a population that is not normally distributed, then irrespective of the shape of the population sampled, the sampling distribution of the sample mean would approach normality with the mean,

¯x that is equal to the population mean, μ, and the standard error of the sampling means would be σ¯x=σ/√n

Now, if the sample size is increased from 100 to 1600, then the denominator of the standard error formula increases, and as a result the standard error value decreases.