Decision Tree Analysis

Question

The management of a bank is concerned about the potential loss that might occur in the event of a hurricane. The bank estimated that the loss from one of these storms could be as much as \$100 million including losses due to interrupted service and customer relations. One project the bank is considering is the installation of an emergency power generator at its operations headquarters. The cost of the emergency generator is \$800,000, and if it is installed no losses from this type of storm will be incurred.

However, if the generator is not installed, there is a 10% chance that a power outage will occur during the next year. If there is an outage there is a 5% probability that the resulting losses will be very large or approximately \$80 million in lost earnings. Alternatively, it is estimated that there is a 95% probability of only slight losses of around \$1 million. Using decision tree analysis with EMV, determine whether the bank should install the new power generator.

Question

The posted speed limit on Interstate 70 is 70 miles per hour,   but it is claimed that the mean of the actual speeds of vehicles is greater   than 70 miles per hour. To test this claim, the speeds of 36 randomly   selected vehicles were taken and reported to the right.

Speed of Randomly Selected Vehicles on I-70   68 77 65 71 77 73     62 78 68 72 77 72     74 72 74 70 76 72     73 71 75 70 70 74     75 61 74 72 69 75     84 79 83 75 71 76

(a)       Give   the null and alternative hypotheses for this situation in mathematical   notation.

(b)       Based upon a 10% level of significance, determine the critical   value(s) associated with this hypothesis test.

(c)       Determine   the sample’s test statistic.

(d)      State a   final conclusion regarding the results of the hypothesis test. Make sure your statement is tied to the   context of the problem (speed of vehicles on I-70).

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