Question

A tax assessor wants to assess the mean property tax bill for all homeowners in Mount Olympus. Based upon previous studies the tax assessor will assume that the population standard deviation is 735 drachma. How many tax records should be sampled if we want to be 95% confident that the sample mean tax bill is within 101 drachma? Assume the population is normally distributed.

Answer 1

population standard deviation ( )= 735

confidence level = 95%

Margin of error (E) = 101

formula for sample size is

Where is the Z critical valu for c=95%

c=95%= 0.95,

= 1- c = 1- 0.95 = 0.05

= 0.05/2 = 0.025

using normal z table we get critical value as

= 1.96

now put all values in formula

n = 203.4436

round it to the next integer

n = 204

Number of tax records should be sampled = 204