Consider the file data on Taxes that is included in worksheet P2 on the exam template. This data represents property taxes paid by 170 residents that live in a small town. Assume this file to be the entire population. Answer the following questions :

a) A local politician in this town has stated that the average property taxes are $1800 and most people do not pay more than this amount. Conduct a test at the alpha = .01 level to determine if this is true. For this test, consider a sample size of 30 households. Also, you want to have strong evidence to disclaim his hypothesis.

b) Find the probability of a Type two error when U = 2200.

c) Conduct the same test as in part a, however, use sampling data by taking the fist 50 data points in the population

d) Conduct a test at the alpha = .05 level to determine if there is a difference between taxes paid in neighborhood 1 and in neighborhood 4. Use all the data points from both neighborhoods and consider this to be sample data.

e) From part d, what is the 95% confidence interval for the difference between means.