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Question
NARRBEGIN: SA_62_64Q-Mart is interested in comparing its male and female customers. Q-Mart would like to know if its female charge customers spend more money, on average, than its male charge customers. They have collected random samples of 25 female customers and 22 male customers. On average, women charge customers spend $102.23 and men charge customers spend $86.46. Some information are shown below.
| Summary statistics for two samples | ||
| Female | Male | |
| Sample sizes | 25 | 22 |
| Sample means | 102.23 | 86.46 |
| Sample standard deviations | 93.393 | 59.695 |
| Confidence interval for difference between means | ||
| Sample mean difference | 15.77 | |
| Pooled standard deviation | 79.466 | |
| Std error of difference | 23.23 | |
(A) Use a t - value of 2.014 to calculate a 95% confidence interval for the difference between the average female purchase and the average male purchase. Would you conclude that there is a significant difference between females and males in this case? Explain.
(B) What are the degrees of freedom for the t-multiple in this calculation? Explain how you would calculate the degrees of freedom in this case.
(C) What is the assumption in this case that allows you to use the pooled standard deviation for this confidence interval?
Answer
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NARRBEGIN: SA_55_62A landowner in Texas is offered $200,000 for the exploration rights to oil on her land, along with a 25% royalty on the future profits if oil is discovered. The landowner is also tempted to develop the field herself, believing that the interest in her land is a good indication that oil is present. In that case, she will have to contract a local drilling company to drill an exploratory well on her own. The cost for such a well is $750,000, which is lost forever if no oil is found. If oil is discovered, however, the landowner expects to earn future profits of $7,500,000. Finally, the landowner estimates (with the help of her geologist friend) the probability of finding oil on this site to be 60%.NARREND(A) Construct a decision tree to help the landowner make her decision. Make sure to label all decision and chance nodes and include appropriate costs, payoffs and probabilities.(B) What should the landowner do? Why?(C) Suppose the landowner is uncertain about the reliability of her geologist friend's estimate of the probability that oil will be found on her land. If she thinks the probability could be anywhere between 40% and 80%, would that change her decision?(D) Suppose that, in addition to the uncertainty about the probability of finding oil, the landowner is also uncertain about the cost of the exploratory well (could vary +/- 25%) and the future profits (could vary +/- 50%). To which of these variables is the expected value most sensitive?(E) What does the risk profile show about the relative risk levels for the landowner's two options?(F) Suppose the landowner suspects that she may be a somewhat risk-averse decision maker, because the she doesn"t feel there is as much of a difference between the two options as their expected values would indicate. She consults with a decision analysis expert who asks her to decide between two hypothetical alternatives: 1) a gamble with equal probabilities of winning an amount $X and losing an amount "$X/2, and 2) doing nothing, with a payoff of $0. The point at which she cannot decide between 1) and 2) is when X=$1,500,000. What is her risk tolerance if she uses an exponential utility function to model her preferences?(G) Apply the risk tolerance given in your answer to the previous question to the landowner's decision tree in (A). What is the optimal decision in this case? What is the resulting certainty equivalent?(H) If the landowner could hire an expert geologist prepare a report to help her make her decision, what is the most that information could be worth? Assume the geologist's information is perfectly reliable.
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