Question

1. Contingency table. For the following table that has frequencies from counties and their health outcomes, find the probability of a bad health outcome if you were to live in a rural county.

   	bad	good
   rural	501	68
   urban	103	391

2. Binomial probability. About 2% of the time you would expect to succumb to an infection that keeps you from going to work in any given week. What is the probability of being out due to this event exactly once in a 10 week period?
3. Uniform distribution. You have no idea about the shape of the distribution of your stock portfolio. You do know that it can range from 10,000 to 15,000 dollars in a 52 week period. What is mean and standard deviation you can expect if you repeatedly (and maybe even annoyingly!) sampled the opinions of 5 expert portfolio managers?
4. Normal distribution Mid-term grades averaged 74 with a standard deviation of 7. It was such a hard exam that the professor strongly felt that 5% of the students should get an A for their heroic efforts. What is the cut off grade for A's?
5. Confidence Interval -- known population variance. You sample 100 workers in a warehouse that employs 2,000 workers. You find that 60 prefer to form a collective bargaining unit (that is, join a labor union). What is the 95% confidence interval for the proportion of all workers in the warehouse who prefer to form a collective bargaining unit?
6. Confidence interval -- sampled variance. A random sample of 9 application specific integrated circuit (ASIC) chips for inventory control were found to have a mean life of 3,000 operating hours with a standard deviation of 450 hours. The typical ASIC chip standard deviation has never been reported by the manufacturer. What is the confidence interval for the mean life of the entire shipment?
7. Hypothesis testing -- known population variance. You purchase 9 cans of so-called salt-free tomato sauce to test the manufacturer's claim that there is no more than 35 grams of sodium in each can. The manufacturer also claims that there is a standard deviation of 4 grams for all cans shipped during the past 12 months. Your analysis indicates that there is a mean of 40 grams in your sample. Should you accept the manufacturer's claim at the 95% level?
8. Hypothesis testing -- sampled variance. You purchase 9 cans of so-called salt-free tomato sauce to test the manufacturer's claim that there is no more than 35 grams of sodium in each can. Your analysis indicates that there is a mean of 40 grams with a standard deviation of 7 grams of sodium in your sample. You do not believe the manufacture's claim that there is only a standard deviation of 4 grams in the so-called population.of all cans produced. Should you accept the manufacturer's claim at the 95% level? (Use =T.INV() in Excel to compute the critical t-score).
9. Regression -- slope confidence interval. What is the 95% range of sampled elasticities of the influence of lot size on Bronx housing prices if the sampled mean of slopes is 0.53 with a standard deviation of 0.39? There are 14 observations of prices and lot sizes. (Use =T.INV() in Excel to compute the critical t-score).
10. Regression -- slope hypothesis test. Is the sampled elasticity of the influence of lot size on Bronx housing prices meaningful? That is, is the sampled mean elasticity significantly different from zero? The sampled mean of slopes is 0.53 with a standard deviation of 0.39. There are 14 observations of prices and lot sizes. (Use =T.INV() in Excel to compute the critical t-score).

Answer 1