5. Mean Property Tax: A tax assessor wants to estimate the mean property tax bil

Question

5. Mean Property Tax: A tax assessor wants to estimate the mean property tax bill for all homeowners in Madison, Wisconsin. A survey ten years ago got a sample mean of $1400 and a sample standard deviation of $995 based on 250 random surveys a) (a) E stimate the population mean of property taxes for all homeowners in Madison Wisconsin with a level of confidence of 95%. Sample Size n= b) (b) Suppose the assessor wants to estimate the property tax for homeowners within $100. How many surveys must the assessor collect in order to get to this margin or error at a level of confidence at 95%?

Explanation / Answer

Part a

Here, we have to find 95% confidence interval for population mean.

Confidence interval = Xbar -/+ t*S/sqrt(n)

We are given

Xbar = 1400

S = 995

n = 250

DF = n – 1 = 250 – 1 = 249

Confidence level = 95% ( = 0.05)

Critical t value = 1.9695

(By using t-table or excel)

Confidence interval = 1400 -/+ 1.9695*995/sqrt(250)

Confidence interval = 1400 -/+ 1.9695*62.92932544

Confidence interval = 1400 -/+ 123.9416

Lower limit = 1400 - 123.9416 = 1276.058

Upper limit = 1400 + 123.9416 = 1523.942

Confidence interval = (1276.058, 1523.942)

Part b

Here, we have to find sample size. Sample size formula is given as below:

n = (Z* / E)^2

We are given

= 995

E = 100

Confidence level = 95%

Z = 1.96 (by using z-table)

n = (1.96*995/100)^2 = 380.328

Required sample size = 381

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