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mathematics
statistics

Questions and Answers of Statistics

Here are data relating the carbon footprint (tons of CO2 per year) to the new Environ-mental Protection Agency (EPA) highway mileage for 82 family sedans as reported by the U.S. government
The Office of Federal Housing Enterprise Oversight (www.ofheo.gov) collects data on various aspects of housing costs around the United States.Here is a scatterplot of the Housing Cost Index versus
Since 1980, average mortgage interest rates have fluctuated from a low of under 4% to a high of over 14%. Is there a relationship between the amount of money people borrow and the interest rate
For which one of the following situations would a Wilcoxon rank-sum (or Mann-Whitney) test be appropriate? a) The Mohs scale rates the hardness of minerals. If one mineral can scratch another, it is
For which one of the following situations would a Kruskal Wallace test be appropriate? a) Comparing the ratings of a new product on a 5-point Likert scale by a panel of consumers to their ratings of
For which one of the following situations would a Kruskal-Wallace test be appropriate? a) The Mohs scale rates the hardness of minerals. If one mineral can scratch another, it is judged to be harder.
For which one of the following situations would a Wilcoxon signed-rank test be appropriate? a) Comparing the ratings of a new product on a 5-point Likert scale by a panel of consumers to their
For which one of the following situations would a Wilcoxon signed rank test be appropriate? a) The Mohs scale rates the hardness of minerals. If one mineral can scratch another, it is judged to be
For which one of the following situations would Kend all's tau be appropriate? a) Comparing the ratings of a new product on a 5-point Likert scale by a panel of consumers to their ratings of a
In Chapters 4 and 13 we considered what factors might contribute to the price of a home. In Chapter 4 we looked at living area and in Chapter 13 we considered such features as whether the home had a
Which of the following are Actions and which are States of Nature? a) Whether Unemployment is above or below 10%. b) Whether a new product should be brought to market before or after the beginning of
For the probabilities of Exercise 8 and the decision tree of Exercise 4, using the expected values found in Exercise 8, compute the standard deviations of the values associated with each action and
You are planning a trip home at the end of the semester and need to make plane reservations soon. However, you’ve just had a preliminary interview with a consulting firm that seemed to go very
A small company has the technology to develop a new personal data assistant (PDA), but it worries about sales in the crowded market. They estimate that it will cost $600,000 to develop, launch, and
After a series of extensive meetings, several of the key decision makers for a small marketing firm have produced the following payoff table (expected profit per customer) for various advertising
An investment bank is thinking of investing in a start-up alternative energy company. They can become a major investor for $6M, a moderate investor for $3M, or a small investor for $1.5M. The worth
Construct a decision tree for the payoff table in Exercise 11. In Exercise You are planning a trip home at the end of the semester and need to make plane reservations soon. However, you’ve just had
Construct a decision tree for the payoff table in Exercise 12.In exerciseA small company has the technology to develop a new personal data assistant (PDA), but it worries about sales in the crowded
If you think the probability of being called for an interview is 0.30, calculate the expected value of each action in Exercise 15. Which is the better action in this case?
An analyst for the company in Exercise 12 thinks the probabilities of high, moderate, and low sales are 0.2, 0.5, and 0.3, respectively. In this case calculate the expected value of each action.
For the decision of Exercise 11, you’ve just learned that you are on the short list and now estimate the chance that you’ll be called for an interview is 0.70. Does that change your choice of
Which of the following are Actions and which are States of Nature? a) Whether to invest in solar energy companies. b) Whether your chief competitor decides to launch a new advertising campaign. c)
For the product launch decision of Exercise 12, the economy isn’t looking that good. Your very cautious boss says that he thinks there’s a 60% chance of low sales, and a 30% chance of moderate
For the payoff table in Exercise 13, find the action with the highest expected value.In exercisea) If forecasters think the probability of rising consumer confidence is 0.70, what is its expected
a) For the payoff table in Exercise 14, find the investment strategy under the assumption that the probability that the price of oil goes substantially higher is 0.4 and that the probability that it
a) For the advertising strategies of Exercise 21 and using the probability of 0.70 for rising consumer confidence, what is the Expected Value of Perfect Information (EVPI)?In exerciseb) What is the
For the energy investment of Exercise 22 and using both of the probabilities considered in that exercise, find the Expected Value of Perfect Information.In exerciseAn investment bank is thinking of
The company from Exercises has the option of hiring an economics consulting firm to predict consumer confidence. The company has already considered that the probability of rising consumer confidence
The company in Exercises 14, 22, and 24 could send a team to Saudi Arabia to obtain additional information about the probabilities that oil will increase or decrease in price. They hope that the
KickGrass Lawncare is a service that cares for lawns in a large, affluent community. Shawn Overgrowth, the owner, is considering the purchase of new zero-turn riding lawn tractors, which would allow
Demand and price are related; raising prices typically lowers demand. Many companies understand that if they can segment their market and offer different prices to different segments, they can often
You are called on to decide how your company should produce its new cell phone screen defroster (for use by skiers and others spending time out of doors in the cold.) You develop the following cost
Aaron’sAir (Exercises) estimates that high-demand periods (which depend on the weather and on bookings for conferences) occur with probability .3 and medium demand periods occur with probability
Aaron’sAir (Exercises) could purchase a market survey from a firm that has advised the island tourist and conference bureau. He thinks their projections would help him determine whether the
An investor is considering adding a stock to her portfolio. Assuming she buys 100 shares, here is an estimated payoff table for the alternative stocks if she holds onto them for six months. The value
An investor is considering how to invest her money. She has two options€”either a domestic mutual fund that only invests in blue chip stocks or an international aggressive mutual fund that
A bicycle shop owner is deciding which products to stock. His distributor will give him a deal if he buys more of the same kind of bike. The payoff table shows monthly sales for a high-end bike
The bike shop owner has now done a bit more research and believes that the demand for high-end bikes has shifted, so that now the low demand is 50% likely and the high demand is only 10% likely. How
Here is a decision tree for the profits (in $000€™s) you project for your sales of the cell phone screen defroster, depending on the weather this coming winter and your choice of
For the cost matrix of Exercise 3,In exercisea) What is the minimax choice? b) What is the minimin choice?
For the decision tree of Exercise 4,In exercisea) What is the maximin choice? b) What is the maximax choice?
For the cost matrix of Exercise 3,In exercisea) Suppose P(Recession) = 0.2, P(Stable) = 0.2, and P(Expansion) = 0.6. What is the expected value of each action? b) What is the best choice using the
For the decision tree of Exercise 4,In exercisea) Suppose P(Warm) = 0.5, P(Moderate) = 0.3, and P(Cold) = 0.2. What is the expected value of each action? b) What is the best choice using the
For the probabilities of Exercise 7 and the cost matrix of Exercise 3, using the expected values you found in Exercise 7, compute the standard deviation of values associated with each action and the
“Oil is big business.” A classic example of this is the Texaco-Pennzoil court case, which appeared in the book Making Hard Decisions5 and in a subsequent case study by T. Reilly and N. Sharpe
InterCon Travel Health is a Toronto-based company that provides services to health insurers of foreign tourists who travel to the United States and Canada.7 As described in the Guided Example in this
Explain the difference between descriptive and inferential statistics.
List the four major methods of collecting data, and explain their differences.
Explain how populations and variables differ.
What is a representative sample? What is its value?
Colleges and universities are requiring an increasing amount of information about applicants before making acceptance and financial aid decisions. Classify each of the following types of data
In the Journal of Earthquake Engineering (Nov. 2004), a team of civil and environmental engineers studied the ground motion characteristics of 15 earthquakes that occurred around the world since
The Sport Journal (Winter 2004) reported on a study of a speed-training program for high school football players. Each participant was timed in a 40-yard sprint both before and after training. The
Consider the set of all students enrolled in your statistics course this term. Suppose you’re interested in learning about the current grade point averages (GPAs) of this group. a. Define the
Biologists at the University of California (Riverside) are studying the patterns of extinction in the New Zealand bird population. (Evolutionary Ecology Research, July 2003.) At the time of the Maori
The American Association of Nurse Anesthetists Journal (Feb. 2000) published the results of a study on the use of herbal medicines before surgery. Of 500 surgical patients randomly selected for the
All highway bridges in the United States are inspected periodically for structural deficiency by the Federal Highway Administration (FHWA). Data from the FHWA inspections are compiled into the
The Computer Security Institute (CSI) conducts an annual survey of computer crime committed at U.S. businesses. CSI sends survey questionnaires to computer security personnel at all U.S. corporations
According to the American Lung Association, lung cancer accounts for 28% of all cancer deaths in the United States. A new type of screening for lung cancer, computed tomography (CT), has been
A recent survey conducted for the National Association of Broadcasters investigated satellite radio subscriber service and usage. The June 2007 survey, conducted by Wilson Research Strategies,
Does a massage enable the muscles of tired athletes to recover from exertion faster than usual? To answer this question, researchers recruited eight amateur boxers to participate in an experiment.
Is insomnia related to education status? Researchers at the Universities of Memphis, Alabama at Birmingham, and Tennessee investigated this question in the Journal of Abnormal Psychology (Feb. 2005).
The effect of the emotion of guilt on how a decision maker focuses on a problem was investigated in the Journal of Behavioral Decision Making (January 2007). A total of 155 volunteer students
Are men or women more adept at remembering where they leave misplaced items (such as car keys)? According to University of Florida psychology professor Robin West, women show greater competence in
The PROMISE Software Engineering Repository, hosted by the University of Ottawa, is a collection of publicly available data sets to serve researchers in building prediction software models. A PROMISE
“Have you ever seen anything that you believe was a spacecraft from another planet?” This was the question put to 1,500 American adults in a national poll conducted by ABC News and The Washington
Explain the difference between a bar graph and a pie chart.
In The Canadian Journal of Information and Library Science (Vol. 33, 2009), researchers from the University of Western Ontario reported on mall shoppers€™ opinions about libraries and their
The characteristics of cheek teeth (e.g., molars) can provide anthropologists with information on the dietary habits of extinct mammals. The cheek teeth of an extinct primate species was the subject
In grade school, did your teacher have a pet in the classroom? Many teachers do so in order to promote humane education. The Journal of Moral Education (Mar. 2010) published a study designed to
Personal identification number (PIN) pads are devices that connect to point-of-sale electronic cash registers for debit and credit card purchases. The PIN pad allows the customer card to be accessed
Writing in the Journal of Family History (Jan. 2010), Hong Kong University historian Sangkuk Lee investigated the genealogy of a certain Korean clan. Of interest to Lee was whether or not a family
Archaeologists excavating the ancient Greek settlement at Phylakopi classified the pottery found in trenches. (Chance, Fall 2000) The accompanying table describes the collection of 837 pottery pieces
University of New Mexico professor Jane Hood investigated the fieldwork methods used by qualitative sociologists. (Teaching Sociology, July 2006) Searching for all published journal articles,
In its annual General Social survey (GSS), the National Opinion Research Center (NORC) elicits the opinions of Americans on a wide variety of social topics. One question in the survey asked about a
Refer to the Evolutionary Ecology Research (July 2003) study of the patterns of extinction in the New Zealand bird population, Exercise. Data on flight capability (Volant or flightless), habitat
Explain the difference between a bar graph and a histogram.
Graph the relative frequency histogram for the 500 measurements summarized in the accompanying relative frequency table. Class Interval Relative Frequency .5–2.5 ............... .10 2.5–4.5
Consider the MINITAB histogram shown below.a. Is this a frequency histogram or a relative frequency histogram? Explain. b. How many class intervals were used in the construction of this histogram?
Does a teaspoon of honey before bed really calm a child's cough? To test the folk remedy, pediatric researchers at Pennsylvania State University carried out a designed study involving a sample of 105
Refer to the American Journal of Physical Anthropology (Vol. 142, 2010) study of the characteristics of cheek teeth (e.g., molars) in an extinct primate species, Exercise. In addition to degree of
Lichen has a high absorbance capacity for radiation fallout from nuclear accidents. Since lichen is a major food source for Alaskan caribou, and caribou are, in turn, a major food source for many
Crab spiders use camouflage to hide on flowers while lying in wait to prey on other insects. Ecologists theorize that this natural camouflage also enables the spiders to hide from their own
Data from a psychology experiment were reported and analyzed in The American Statistician (May 2001). Two samples of female students participated in the experiment. One sample consisted of 11
Educators are constantly evaluating the efficacy of public schools in the education and training of U.S. students. One quantitative assessment of change over time is the difference in scores on the
A data set contains the observations 5, 1, 3, 2, 1. Find a. ∑x b. ∑x2 c. ∑(x –1) d. ∑(x –1)2 e. (∑x)2
Refer to Exercise 2.44. Find a. ∑x2 – (∑x2) / 5 b. ∑(x – 2)2 c. ∑x2 – 10
Explain the concept of a skewed distribution.
Calculate the mean and median of the following grade point averages:3.2 2.5 2.1 3.7 2.8 2.0Calculate the mode, mean, and median of the following data:18 10 15 13 17 15 12 15 18 16 11
Construct one data set consisting of five measurements, and another consisting of six measurements, for which the medians are equal.
Calculate the mean, median, and mode for each of the following samples: a. 7, −2, 3, 3, 0, 4 b. 2, 3, 5, 3, 2, 3, 4, 3, 5, 1, 2, 3, 4 c. 51, 50, 47, 50, 48, 41, 59, 68, 45, 37
Fortune (Oct. 16, 2008) published a list of the 50 most powerful women in business in the United States. The data on age (in years) and title of each of these 50 women are stored in the WPOWER50
Refer to the Archives of Pediatrics and Adolescent Medicine (Dec. 2007) study of honey as a remedy for coughing, exercise. Recall that the 105 ill children in the sample were randomly divided into
A group of Northeastern University researchers developed a new method for ranking the total driving performance of golfers on the Professional Golf Association (PGA) tour (The Sport Journal Winter
Would you expect the data sets that follow to possess relative frequency distributions that are symmetric, skewed to the right, or skewed to the left? Explain. a. The salaries of all persons
The Journal of Biogeography (Dec. 2003) published an article on the first comprehensive study of ants in Mongolia (Central Asia). Botanists placed seed baits at 11 study sites and observed the ant
The U.S. Energy Information Administration monitors all nuclear power plants operating in the United States. The table below lists the number of active nuclear power plants operating in each of a
What is the primary disadvantage of using the range to compare the variability of data sets?
Can the variance of a data set ever be negative? Explain. Can the variance ever be smaller than the standard deviation? Explain.
Calculate the variance and standard deviation for samples for which a. n = 10 , ∑x2 = 84, ∑x = 20 b. n = 40, ∑x2 = 380, ∑x = 100 c. n = 20, ∑x2 = 18, ∑x = 17

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