Question

Suppose x has a normal distribution with mean μ = 31 and standard deviation σ = 11.

Describe the distribution of x values for sample size n = 4. (Round σ_x to two decimal places.)

μx	=
σx	=

Describe the distribution of x values for sample size n = 16. (Round σ_x to two decimal places.)

μx	=
σx	=

Describe the distribution of x values for sample size n = 100. (Round σ_x to two decimal places.)

μx	=
σx	=

How do the x distributions compare for the various samples sizes?

The standard deviations are the same, but the means are increasing with increasing sample size.The means are the same, but the standard deviations are increasing with increasing sample size.    The means are the same, but the standard deviations are decreasing with increasing sample size.The standard deviations are the same, but the means are decreasing with increasing sample size.The means and standard deviations are the same regardless of sample size.

Answer 1

We know , if , then , for a sample of size n ,

Thus , for , then ,

i ) For , n = 4 ,

ii ) For , n = 16,

iii ) For , n = 100 ,

The means are the same, but the standard deviations are decreasing with increasing sample size.