(i) What proportion of branches are profitable? (ii) What proportion of branches from an urban location are profitable? (iii) What proportion of branches from a rural location are profitable?
Question 1
Show all your work. Indicate clearly the methods you use, because you will be scored on the correctness of your methods as well as on the accuracy and completeness of your results and explanations.
A large national bank determines if each of its branches is profitable or not profitable. Additionally, the location of each branch is classified as urban, suburban, or rural. A summary of the profitability and location type of a random sample of 175 of the bank’s branches is shown in the table.
| Profitable | Not Profitable | |
| Urban | 64 | 17 |
| Suburban | 39 | 22 |
| Rural | 18 | 15 |
(a) From the sample of 175 branches summarized above:
- (i) What proportion of branches are profitable?
- (ii) What proportion of branches from an urban location are profitable?
- (iii) What proportion of branches from a rural location are profitable?
Question 2
(b) Assuming the conditions for inference are met, does the data provide convincing statistical evidence that profitability and location type are independent for the bank at a 5 percent level of significance? Complete the appropriate inference procedure to support your answer.
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