Problem #1

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 all of the following questions :

a. Conduct a test at the alpha = .05 level to determine if there is a difference in taxes paid by another jurisdiction. The information on this other jurisdiction is population information. In this other jurisdiction, the mean taxes paid by 243 residents are $1751.68 with a population standard deviation of $141.62. State Ho and Ha, Critical T or Z, and the decision.

b. What is the 95% confidence interval for the difference between the taxes paid in the two jurisdictions from problem a. State the upper and lower limits.

c. 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. State Ho and Ha, Critical T or Z, Calculated T or Z, and the decision.

d. From part c, what is the 95% confidence interval for the difference between means in the two neighborhoods. State the upper and lower limits.

e. For part c, conduct a test at alpha = .05 to see if the variances between the two neighborhoods are unequal. State F Critical, F Test, and the decision.

Problem #2

An engineering statistician wants to conduct a test to determine if there is a difference in the compression strength of two different manufactures of reinforced concrete columns. Each manufacturer has provided sample data for compression strength (column failure) as follows:

Manufacturer 1: mean compression strength is 956 KSI based on 30 samples with a standard deviation of 192 KSI.

Manufacturer 2: mean compression strength of 898 KSI based on 25 samples with a standard deviation of 256 KSI

Conduct a test at alpha equal to .01 to see if there is a difference between the two different manufacturers. Consider the data to be from two different populations. State Ho and Ha, Critical T or Z, Calculated T or Z, p Value, and the decision.

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