Unlock document.
This document is partially blurred.
Unlock all pages and 1 million more documents.
Get Access
If we draw a straight line through the points in a scatterplot and most of the points fall
close to the line, there is a strong positive linear relationship between the two variables.
The expected value of sample information (EVSI) is the difference between the EMV
we can obtain with sample information and the EMV we can obtain without
information.
NARRBEGIN: SA_90_91
The following is a payoff table giving profits for various situations:
States of Nature
The probabilities for states of nature A, B, and C are 0.3, 0.5, and 0.2 respectively.
NARREND
What are the expected payoffs for the three alternatives?
Utility function is a function that encodes a person's or company's feelings toward risk.
NARRBEGIN: SA_57_64
Amanda is a recent college graduate, and has just started her first job. She would like to
know if she saves $5,000 per year out of her salary over the next 30 years what the
distribution of the value of her retirement fund after 30 years. She has decided that she
will invest all her money in the stock market that she estimates has a return that is
normally distributed with mean 12% per year and standard deviation 25%.
NARREND
Suppose Amanda will stop investing in the stock market and transfer all of her
retirement into a savings account if and when she reaches $500,000. When can she
expect to reach this goal?
The slope of the lines for the input variables on a tornado chart indicates their relative
impact on the expected value
A null hypothesis is a statement about the value of a population parameter. It is usually
the current thinking, or "status quo".
NARRBEGIN: SA_104_113
Suppose that patrons of a restaurant were asked whether they preferred beer or whether
they preferred wine. 60% said that they preferred beer. 70% of the patrons were male.
80% of the males preferred beer.
NARREND
Construct the joint probability table.
NARRBEGIN: SA_68_73
Suppose that GM earns a $4000 profit each time a person buys a car. We want to
determine how the expected profit earned from a customer depends on the quality of
GM's cars. The customer is assumed to buy a new car every five years, for a total of 10
cars through her lifetime. The customer will keep buying GM cars so long as they are
satisfied with them. The probability that the customer will be satisfied with her GM car
is 80%. If she is not satisfied with her GM car, she will buy another brand (we"ll call all
other brands cumulatively "Toyota"). The probability that she is satisfied with "Toyota"
is 85%.
NARREND
Suppose that a customer satisfaction firm approaches GM with a proposal to increase
satisfaction from the current 80% rate to $85% through a low cost maintenance
program that will cost GM $300 per customer. Would the program be worth it?
NARRBEGIN: SA_108_112
The following values have been calculated using the TDIST and TINV functions in
Excel. These values come from a t- distribution with 15 degrees of freedom.
These values represent the probability to the right of the given positive values.
These values represent the positive t- value for a given probability in both tails (sum of
both tails).
NARREND
You are trying to estimate the average amount a family spends on food during a year. In
the past the standard deviation of the amount a family has spent on food during a year
has been approximately $800. If you want to be 95% sure that you estimated average
family food expenditures within $50, how many families do you need to survey?
If a constraint has the equation , then the constraint line passes through the
points (0,20) and (30,0):
Although we can determine the optimal bid and the expected profit from that bid in a
bidding simulation, we usually cannot determine the probability of winning.
NARRBEGIN: SA_123_125
Suppose that a decision maker's utility as a function of her wealth, x, is given by U(x) =
ln x (the natural logarithm of x).
NARREND
The decision maker now has $10,000 and two possible decisions. For Alternative 1, she
loses $500 for certain (x=$9,500). For Alternative 2, she loses $0 (x=$10,000) with
probability 0.9 and loses $5,000 (x=$5,000) with probability 0.10. Which alternative
maximizes the expected utility of her net wealth?
The percentage of the US population without health insurance coverage for samples
from the 50 states and District of Columbia for both 2003 and 2004 produced the
following table of correlations.
What does the table for the two given sets of percentages tell you in this case?
In marketing and sales models, the primary issue is the uncertain amount of sales that
can be obtained, given an assumed timing.
In regression analysis, the unexplained part of the total variation in the response
variable Y is referred to as sum of squares due to regression, SSR.
NARRBEGIN: SA_74_77
The "winner's curse" refers to a situation where there are several bidders on the same
item. Each participant can make his or her independent estimate for the value of the
item. When all participants are equally informed their estimates will be unbiased, but,
given the difficulty of estimating the value, the estimates may vary widely. Even though
the mean of the estimates may equal the expected value, the winner's bid will likely be
more than the value of the item. Consider a case where 3 companies are trying to decide
how much to bid for a commercial real estate tract. Assume that each bidder
independently estimates the value of the tract. This estimated value is a random variable
that for each bidder is drawn from a normal distribution with a mean of $1,000,000 and
a standard deviation of $200,000. The actual value is also drawn from the same
distribution.
NARREND
What is the probability of winning for each bidder in the above scenario?
Do these data help to confirm or contradict the hypothesis that increased wage
inequality leads to lower unemployment levels? [Hint: construct a scatterplot]
If the coefficient of correlation r = 0 .80, the standard deviations of X and Y are 20 and
25, respectively, then Cov(X, Y) must be 400.
