A car dealer in Big Rapids, Michigan is using Holt’s method to forecast weekly car
sales. Currently the level is estimated to be 45 cars per week, and the trend is estimated
to be 5 cars per week. During the current week, 25 cars are sold. After observing the
current week’s sales, forecast the number of cars three weeks from now. Use
.
NARRBEGIN: SA_113_117
A television network earns an average of $1.6 million each season from a hit program
and loses an average of $400,000 each season on a program that turns out to be a flop,
and of all programs picked up by this network in recent years, 25% turn out to be hits
and 75% turn out to be flops.
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The network can conduct market research to determine whether a program will be a hit
or a flop. If the market research report is perfectly reliable, what is the most the network
should be willing to pay for it?
NARRBEGIN: SA_71_73
A manager for Marko Manufacturing, Inc. has recently been hearing some complaints
that women are being paid less than men for the same type of work in one of their
manufacturing plants. The boxplots shown below represent the annual salaries for all
salaried workers in that facility (40 men and 34 women).
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What can you say about the shape of the distributions given the boxplots above?
The following scatterplot compares the selling price and the appraised value.
Is there a linear relationship between these two variables? If so, how would you
characterize the relationship?
NARRBEGIN: SA_95_100
A recent survey in Michigan revealed that 60% of the vehicles traveling on highways,
where speed limits are posted at 70 miles per hour, were exceeding the limit. Suppose
you randomly record the speeds of ten vehicles traveling on US 131 where the speed
limit is 70 miles per hour. Let X denote the number of vehicles that were exceeding the
limit.
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Find P(X = 2).
Stratified samples are typically not used in real applications because they provide less
accurate estimates of population parameters for a given sampling cost.
One of the primary advantages of simulation models that they enable managers to
answer what-if questions about changes in systems without actually changing the
systems themselves.
In an additive seasonal model, we add an appropriate seasonal index to a “base”
forecast. These indexes, one for each season, typically average to 0.
If the standard error of the sampling distribution of the sample proportion is 0.0324
for samples of size 200, then the population proportion must be 0.30.
A moving average is the average of the observations in the past few periods, where the
number of terms in the average is the span.
NARRBEGIN: SA_86_91
In this example we are estimating the net present value of introducing a new drug to
market. We have the following information about the market:
The market size is 1,000,000 and is projected to grow at an average 5%, with a standard
deviation of 1%, over the next ten years.
The market share captured at entry is projected to be between 20% and 70%, with most
likely value 40%.
Three competitors may enter the market in the future, with each one having a 40%
probability of entry per year.
For each new competitor per year, the market share goes down by 20%.
The marginal profit per unit is $1.80.
We want to evaluate the project over ten years, using a discount rate of 10%.
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What is the appropriate distribution for the probability of competitor entry?
A regression analysis between sales (in $1000) and advertising (in $100) resulted in the
following least squares line: = 84 +7X. This implies that if there is no advertising,
then the predicted amount of sales (in dollars) is $84,000.
The binomial random variable represents the number of successes that occur in a
specific period of time.