Question

Suppose that the average assessed values of single family dwellings in a large municipality of $165,000 with a standard deviation of $20,000.

a.) If a random sample of n = 100 dwellings is selected and x ¯ , the average assessed value of these dwellings is calculated, what is the mean x ¯ in repeated sampling

b.) What is the standard deviation of x ¯

Answer 1

Solution :

Given that ,

mean = $\mu$ = $165,000

standard deviation = $\sigma$ = $20,000

n = 100

a) $\mu$ _{$\bar x$} = $\mu$ = $165,000

b) $\sigma$ _{$\bar x$} = $\sigma$ / $\sqrt$ n = $20,000 / $\sqrt$ 100 = $2000