Question: Use the following data to answer all parts of this question: A lending institution gives both adjustable-rate (A) mortgages and fixed-rate (F) mortgages on residential property. It breaks residential property into three categories: single-family (S), condominiums (C), and multifamily dwelling (M). The institution desires to learn more about the possibility of a relationship between property category and mortgage type in an effort to increase its appeal to potential customers. Consequently, it hires you to do a very preliminary analysis. The analysis is based on a random sample of 200 of its existing customers. Here is some of the information you have found:

-- 140 of all customers had adjustable rate mortgages; the rest fixed.

-- Of those with adjustable-rate mortgages, 70 had single-family dwellings, 42 had condominiums, and 28 had multifamily dwellings.

-- Of those with fixed-rate mortgages, 30 had single-family dwellings, 18 had condominiums, and 12 had multifamily dwellings.

a) Set up a 2 x 3 frequency contingency table for these data. (Here, 2 x 3 means two rows and three columns). When labeling the respective rows and columns, be sure to use the abbreviated notation presented in the problem description.

b) Take the frequency contingency table in part (b) and convert each item to a probability. (All relevant information that enables you to do this is presented in the problem statement.) Take these results and construct a table similar to the table constructed in part (b). This new table is called the probability contingency table.

c) What is the probability that an individual has an adjustable mortgage. What is the name for this probability? That is, what kind of probability is this?

d) What is the probability that an individual has a fixed-rate mortgage and owns a condominium? What is the name for this probability? That is, what kind of probability is this?

e) What is the probability that an individual has a fixed-rate mortgage or owns a single-family dwelling? Be complete in presenting your computation. What is the name of the rule used for computing this probability?

f) Considering only those who have an adjustable-rate mortgage, what is the probability of an individual owning a multifamily dwelling? Please write this question in “probability notation”. What is the name for this probability? That is, what kind of probability is this?

g) Develop and carry out a test to determine if type of mortgage rate and residential property category are statistically independent. Use your result from part (f) as the basis for your test. Explain in a sentence the logic of your test.