3. Refer to Problem #2. A marketing research company claims that they can determine the exact demand for the product. Compute the EVPI to help Gorman decide whether it should attempt to obtain a better estimate of demand. Nose mach such information worth? What is the maximum amount that Gorman should be willing to pay for the market research? 4. Refer to Problem #2. A test market study of the potential demand for the product is expected to report either a favorable (F) or an unfavorable (U) condition. The relevant conditional probabilities are as follows: P(F|$s_1$) = 0.10 P(U|$s_1$) = 0.90 P(F|$s_2$) = 0.40 P(U|$s_2$) = 0.60 P(F|$s_3$) = 0.60 P(U|$s_3$) = 0.40 a. What is the unconditional probability that the market research report will be favorable? [Hint: We can find this value by summing the joint probability values as follows: P(F) = P(F \cap $s_1$) + P(F \cap $s_2$) + P(F \cap $s_3$) = P($s_1$)P(F|$s_1$) + P($s_2$)P(F|$s_2$) + P($s_3$)P(F|$s_3$).]
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Step 1: To find the unconditional probability of a favorable report, we need to sum the joint probabilities of each state. Show moreā¦
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Foton Inc. is going to decide whether to purchase or lease an equipment for its R&D department. The equipment will be used for launching a new product that may have a high or a low demand. The profits (in thousands of dollars) and prior probabilities of the states of demand are shown below. States of Demand and Probabilities High (0.65) s1 Low (0.35) s2 Decision Alternative Purchase, d1 70 10 Lease, d2 50 30 a) Recommend a decision for Foton based on expected values. b) What is the expected value of perfect information (EVPI)? c) A Marketing Research firm offers a telephone survey that may produce a favorable (F) or an unfavorable (U) report for $1000 with the following probabilities. P(F) = ? P(s1|F) = ? P(s1|U) = ? P(U) = 0.20 P(s2|F) = 0.25 P(s2|U) = 0.85 Find the missing probabilities above. d) What is the expected value of Sample Information?
Areen D.
The Gorman Manufacturing Company must decide whether to manufacture a component part at its Milan, Michigan, plant or purchase the component part from a supplier. The resulting profit is dependent upon the demand for the product. The following payoff table shows the projected profit (in thousands of dollars). The state-of-nature probabilities are $P\left(s_{1}\right)=.35, P\left(s_{2}\right)=.35,$ and $P\left(s_{3}\right)=.30$ a. Use a decision tree to recommend a decision. b. Use EVPI to determine whether Gorman should attempt to obtain a better estimate of demand. c. $\quad$ A test market study of the potential demand for the product is expected to report either a favorable $(F)$ or unfavorable $(U)$ condition. The relevant conditional probabilities are as follows: $\begin{array}{ll}P\left(F | s_{1}\right)=.10 & P\left(U | s_{1}\right)=.90 \\ P\left(F | s_{2}\right)=.40 & P\left(U | s_{2}\right)=.60 \\ P\left(F | s_{3}\right)=.60 & P\left(U | s_{3}\right)=.40\end{array}$ What is the probability that the market research report will be favorable? d. What is Gorman's optimal decision strategy? e. What is the expected value of the market research information?
The Gorman Manufacturing Company must decide whether to manufacture a component part at its Milan, Michigan, plant or purchase the component part from a supplier. The resulting profit is dependent upon the demand for the product. The following payoff table shows the projected profit (in thousands of dollars). The state-of-nature probabilities are $P\left(s_{1}\right)=.35, P\left(s_{2}\right)=.35,$ and $P\left(s_{3}\right)=.30$ a. Use a decision tree to recommend a decision. b. Use EVPI to determine whether Gorman should attempt to obtain a better estimate of demand. c. A test market study of the potential demand for the product is expected to report either a favorable $(F)$ or unfavorable $(U)$ condition. The relevant conditional probabilities are as follows: \[ \begin{array}{lll} P\left(F | s_{1}\right)=.10 & P\left(U | s_{1}\right)=.90 \\ P\left(F | s_{2}\right)=.40 & P\left(U | s_{2}\right)=.60 \\ P\left(F | s_{3}\right)=.60 & P\left(U | s_{3}\right)=.40 \end{array} \] What is the probability that the market research report will be favorable? d. What is Gorman's optimal decision strategy? e. What is the expected value of the market research information?
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