Question

# You want to estimate the average household income for Ohio. You want the margin of error...

You want to estimate the average household income for Ohio. You want the margin of error to be no more than \$1,000. Prior data shows the standard deviation of household income is \$30,000.

How many households should we sample to achieve the desired margin of error?

Suppose you want to cut the margin of error down to \$500 next time. What should your sample size be?

Suppose you want to cut the margin down to 1/3 of what it started at (1/3 of 1000). What does your sample sizes have to be? (Be careful!)

Why do we always round up when finding the appropriate sample size to achieve a certain margin of error, even when the value after the decimal point is less than .5? (For example, if we solve for n and get 422.2 households, why do we round this up to 423 households when reporting the required n?)

ME = 1000 , s = 30000

z value at 95% = 1.96

ME = z *(s/sqrt(n))
1000 = 1.96 *(30000/sqrt(n))
n = 3457

ME = 500

z value at 95% = 1.96

ME = z *(s/sqrt(n))
500 = 1.96 *(30000/sqrt(n))
n = 13829

ME = 333.33

z value at 95% = 1.96

ME = z *(s/sqrt(n))
333.33 = 1.96 *(30000/sqrt(n))
n = 31116

If you need part of an any part of it to meet the margin of error requirement, we need the wholw individual. Rounding down will result in a slightly higher margin of error than what you wanted