Question

2. You are working for an oil company, which is exploring a new sub-area for potential oil reserves within the larger Permian basin, which straddles Western Texas and New Mexico. The company has conducted 20 exploratory drills, to test for the presence of oil, and only 2 of the 20 tests has positively indicated the presence of oil. You know that, generally, 5% of drill tests in the Permian basin (1 in 20) will positively indicated the presence of oil, even when there is no major reserve present. The company wants you to tell them if the results so far suggest a new oil reserve, or simply reflect sampling error. (20 Points)

(a) Formulate the company’s research hypothesis, and the null hypothesis. (10 Points)

(b) The company doesn’t want to set up a formal drilling site when no oil reserve exists, because it will waste money. However, it really doesn’t want to pass up drilling when the oil reserve does exist, because it could potentially miss out on billions of dollars. What form of error is the company most worried about? (10 Points)

2.1 A local farm supply store has notices that weekly demand for dicamba during the early growing season is normally distributed, with a mean of 50 and standard deviation of 5. The store usually keeps 60 dicamba kits in stock and re-orders them once a week. (30 Points)

(a) What is the probability that average demand will not be met on a given week? (10 Points)

(b) How many kits should the manager keep in inventory to ensure that they do not run short of demand more than 10% of the time? (10 Points)

(c) After a massive fight broke out between local farmers on dicamba damage, the store notices that dicamba sales are down to 43 kits a week. With what statistical level of confidence can you say that this is a true anomaly, rather than the usual, random variation? (10 Points)

What additional info is needed? Comment unclear?

Answer 1

2.1 (c) Here we'll check 43 is a extreme value: P(X<43) = 0.081. At a level of 5%, we can say that this is not an anomaly. While at level 10% we can say that is an anomaly.