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business
business statistics

Questions and Answers of Business Statistics

Suppose we take the entire sample of ten normal(μ, σ2) observations as a single sample. We will start with the original prior we found in Exercise 15.3.(a) Find the posterior using the macro
In Chapter 3, Exercise 3.7, we were looking at the relationship between log(mass) and log(length) for a sample of 100 New Zealand slugs of the species Limax maximus from a study conducted by Barker
Repeat part (a) with a normal \(\left(304^{2}\right)\) prior, storing the likelihood and posterior in \(\mathrm{c} 5\) and \(\mathrm{c6}\).Data From Exercise 5(a) What are the posterior mean and
Repeat part (a) with a beta(2, 4) prior.[Minitab:] Store the likelihood and posterior in columns c5 and c6 respectively.Data From Exercise 1(a) What are the posterior mean and standard deviation?
Purchasing souvenirs. A major tourist activity is shopping.Travel researchers estimate that nearly one-third of total travel expenditures are used on shopping for souvenirs(Journal of Travel
Refer to the Family and Consumer Sciences Research Journal (Mar. 2005) study of college students and drinking, Exercise 13.57. A second objective of the researchers was to establish a statistical
The Family and Consumer Sciences Research Journal (Mar.2005) published a study of college students and drinking.One of the researchers’ main objectives was to segment college students according to
Excavating ancient pottery. Refer to the Chance (Fall 2000) study of ancient Greek pottery, presented in Exercise 2.186 (p. 134). Recall that 837 pottery pieces were uncovered at the excavation site.
Healing heart patients with music, imagery, touch, and prayer. “Frontier medicine” is a term used to describe medical therapies (e.g., energy healing, therapeutic prayer, spiritual healing) for
Characteristics of ice-melt ponds. Refer to the National Snow and Ice Data Center (NSIDC) collection of data on 504 ice-melt ponds in the Canadian Arctic, presented in Exercise 12.200 (p. 793). One
Museum management. Refer to the Museum Management and Curatorship (June 2010) worldwide survey of 30 leading museums of contemporary art, Exercise 2.22 (p. 69).Recall that each museum manager was
Factors identifying urban counties. The Professional Geographer (Feb. 2000) published a study of urban and rural counties in the western United States. The researchers used six independent
The first-order model E1y2 = b0 + b1 x1 was fit to n = 19 data points. A plot of the residuals of the model is shown.Is the need for a quadratic term in the model evident from the plot? Explain.
Suppose you used MINITAB to fit the model y = b0 + b1 x1 + b2 x2 + e to n = 15 data points and you obtained the printout below.a. What is the least squares prediction equation?b. Find R2 and
Agreeableness, gender, and wages. Refer to the Journal of Personality and Social Psychology (Feb. 2012) study of on-the-job agreeableness and wages, Exercise 12.132(p. 753). Recall that the
State casket sales restrictions. Some states permit only licensed firms to sell funeral goods (e.g., caskets, urns)to the consumer, while other states have no restrictions.States with casket sales
Modeling species abundance. A marine biologist was hired by the EPA to determine whether the hot-water runoff from a particular power plant located near a large gulf is having an adverse effect on
Reality TV and cosmetic surgery. Refer to the Body Image:An International Journal of Research (Mar. 2010) study of the impact of reality TV shows on a college student’s decision to undergo cosmetic
MINITAB was used to fit the model y = b0 + b1 x1 + b2 x2 + e where x1 = e 1 if level 2 0 if not x2 = e 1 if level 3 0 if not to n = 15 data points. The results are shown in the accompanying MINITAB
Commercial refrigeration systems. The role of maintenance in energy savings in commercial refrigeration was the topic of an article in the Journal of Quality in Maintenance Engineering (Vol. 18,
Cooling method for gas turbines. Refer to the Journal of Engineering for Gas Turbines and Power (Jan. 2005) study of a high-pressure inlet fogging method for a gas turbine engine, presented in
Reality TV and cosmetic surgery. Refer to the Body Image:An International Journal of Research (Mar. 2010) study of the impact of reality TV shows on one’s desire to undergo cosmetic surgery,
Predicting runs scored in baseball. Consider a multipleregression model for predicting the total number of runs scored by a Major League Baseball (MLB) team during a season. Using data on number of
MINITAB was used to fit the model y = b0 +b1 x1 + b2 x2 + e to n = 20 data points, and the printout on p. 697 was obtained.a. What are the sample estimates of b0, b1, and b2?b. What is the least
Winning marathon times. In Chance (Winter 2000), statistician Howard Wainer and two students compared men’s and women’s winning times in the Boston LO9 Marathon. One of the graphs used to
Baseball batting averages versus wins. Is the number of games won by a major league baseball team in a season LO9 related to the team’s batting average? Consider data from the Baseball Almanac on
Estimating repair and replacement costs of water pipes.Refer to the IHS Journal of Hydraulic Engineering(Sept. 2012) study of water pipes susceptible to breakage, Exercise 11.28 (p. 628). Recall that
Detecting rapid visual targets. When two targets are presented close together in a rapid visual stream, the second target is often missed. Psychologists call this phenomenon LO9 the attentional
Mongolian desert ants. Refer to the Journal of Biogeography(Dec. 2003) study of ants in Mongolia, presented in Exercise 2.167 (p. 125). Data on annual rainfall, maximum daily temperature, and number
Game performance of water polo players. The journal Biology of Sport (Vol. 31, 2014) published a study of the physiological performance of top-level water polo players.Eight Olympic male water polo
Measuring the moon’s orbit. A handheld digital camera was used to photograph the moon’s orbit and the results summarized in the American Journal of Physics (Apr.2014). The pictures were used to
Do nice guys really finish last? In baseball, there is an old saying that “nice guys finish last.” Is this true in the competitive corporate world? Researchers at Harvard University attempted to
Contaminated fish in the Tennessee River. Refer to the U.S. Army Corps of Engineers data on contaminated fish, saved in the DDT file. The results of an ANOVA and Tukey multiple-comparison analysis to
Rotary oil rigs. An economist wants to compare the average monthly number of rotary oil rigs running in three states: California, Utah, and Alaska. In order to account for month-to-month variation,
Purchase of fair-trade products. “Just-world” theory proposes that people receive the rewards and/or punishments that they deserve. Marketing researchers examined LO4 just-world theory in the
Job satisfaction of STEM faculty. Are university faculty in science, technology, engineering, and math (STEM)disciplines more satisfied with their jobs than non-STEM faculty? And, if so, does this
The following two-way table gives data for a 2 * 3 factorial experiment with two observations for each factor–level combination.Factor B Level 1 2 3 Factor A 1 3.1, 4.0 4.6, 4.2 6.4, 7.1 2 5.9, 5.3
Taste-testing scales. When comparing the palatability of food items, numerical taste test scales are employed. For example, the Hedonic 9-point scale uses the following ratings:1 = dislike extremely,
Evaluating health care research reports. When evaluating research reports in health care, a popular tool is the Assessment of Multiple Systematic Reviews (AMSTAR).AMSTAR, which incorporates 11 items
Solar energy generation along highways. The potential of solar panels on roofs built above national highways as a source of solar energy was investigated in the International Journal of Energy and
A randomized block design was used to compare the mean responses for three treatments. Four blocks of three homogeneous experimental units were selected, and each treatment was randomly assigned to
Bonferroni’s procedure is used to compare the mean distances of the four golf ball brands in Example 10.8. The resulting confidence intervals, with an experimentwise LO4 error rate (EER) of a =
Baking properties of pizza cheese. Due to its unique stretchability, mozzarella is the most commonly used pizza cheese. How do the baking properties of mozzarella compare with those of other pizza
Improving driving performance while fatigued. Can a secondary task—such as a word association task—improve your performance when driving while fatigued?This was the question of interest in a
Study of recall of TV commercials. Do TV shows with violence and sex impair memory for commercials? To answer this question, researchers conducted a designed experiment in which 324 adults were
Soil scouring and overturned trees. Trees that grow in flood plains are susceptible to overturning. This is typically due to floodwaters exposing the tree roots(called soil scouring). Environmental
The United States Golf Association (USGA) regularly tests golf equipment to ensure that it conforms to the association’s standards. Suppose the USGA wishes to compare the mean distances traveled by
Tetrahedral dice. Psychologists sometimes use tetrahedral dice to study our intuition about chance behavior. A tetrahedron (Figure 18.6) is a pyramid with 4 faces, each a triangle with all sides
Rolling a die. Figure 18.5 displays several assignments of probabilities to the six faces of a die. We can learn which assignment is actually correct for a particular die only by rolling the die many
When it rains, it pours. Figure 14.12 plots the highest yearly precipitation ever recorded in each state against the highest daily precipitation ever recorded in that state. The points for Alaska
Comparing correlations. Which of Figures 14.10 and 14.11 has a correlation closer to 1? Explain your answer. Sodium per hot dog (milligrams) 600 500 400 300- 200 o A 100 100 120 0 o 140 160 180
IQ and GPA. Figure 14.10 is a scatterplot of school GPA versus IQ score for all 78 seventh-grade students in a rural Midwest school. Points A, B, and C might be called outliers.(a) Describe the
Three great hitters. Three landmarks of baseball achievement are Ty Cobb’s batting average of .420 in 1911, TedWilliams’s .406 in 1941, and George Brett’s .390 in 1980. These batting averages
Random numbers. If you ask a computer to generate “random numbers”between 0 and 1, you will get observations from a uniform distribution.Figure 13.12 shows the density curve for a uniform
State SAT scores. Figure 12.9 is a histogram of the average scores on the SAT Mathematics exam for students in the 50 states and the District of Columbia in 2004. The distinctive overall shape of
Bias and variability. Figure 3.5 shows the behavior of a sample statistic in many samples in four situations. These graphs are like those in Figures 3.1 and 3.2. That is, the heights of the bars show
The 2000 and 2004 presidential elections. Republican George W.Bush was elected president in 2000 and 2004. Figure 15.6 plots the percentage who voted for Bush in 2000 and 2004 for each of the 50
Web-based exercise. Go to the Congressional Budget Office Web site, www.cbo.gov. What is the current prediction for the federal budget in five years’ time? Is a surplus or a deficit predicted?
Web-based exercise. The best way to develop some feeling for how a regression line fits the points on a scatterplot is to use an applet that allows you to plot and move data points and watch the
Web-based exercise. Find an example of a study in which the issue of association and causation is present. This can be either an example in which association is confused with causation or an example
Always plot your data! A skeptic might wonder if the four very different data sets in Table 15.2 really do have the same correlation and least-squares line. Verify that (to a close approximation) the
Is wine good for your heart? Table 15.1 gives data on wine consumption and heart disease death rates in 19 countries. Verify the equation of the least-squares line given in Exercise 15.13.
The professor swims. Return to the swimming data in Exercise 15.9.(a) Verify the equation given for the least-squares line in that exercise.(b) Suppose you were told only that the pulse rate was 152.
Calculating the least-squares line. Like to know the details when you study something? Here is the formula for the least-squares regression line for predicting y from x. Start with the means x and y
Living on campus. A February 2, 2008, article in the Columbus Dispatch reported a study on the distances students lived from campus and average GPA. Here is a summary of the results:Residence Avg.
Magic Mozart. In 1998, the Kalamazoo (Michigan) Symphony advertised a “Mozart for Minors” program with this statement: “Question: Which students scored 51 points higher in verbal skills and 39
Correlation again. The correlation between IQ score and school GPA(Exercise 15.6) is r = 0.634. The correlation between wine consumption and heart disease deaths (Exercise 15.10) is r = −0.645.
TV watching and school grades. Children who watch many hours of television get lower grades in school on average than those who watch less TV. Suggest some lurking variables that may explain this
Do artificial sweeteners cause weight gain? People who use artificial sweeteners in place of sugar tend to be heavier than people who use sugar.Does this mean that artificial sweeteners cause weight
Is math the key to success in college? Here is the opening of a newspaper account of a College Board study of 15,941 high school graduates:Minority students who take high school algebra and geometry
Health and wealth. An article entitled “The Health and Wealth of Nations” says:The positive correlation between health and income per capita is one of the best-known relations in international
Are big hospitals bad for you? A study shows that there is a positive correlation between the size of a hospital (measured by its number of beds x)and the median number of days y that patients remain
How’s your self-esteem? People who do well tend to feel good about themselves. Perhaps helping people feel good about themselves will help them do better in school and life. Raising self-esteem
Do firefighters make fires worse? Someone says, “There is a strong positive correlation between the number of firefighters at a fire and the amount of damage the fire does. So sending lots of
Lots of wine. Exercise 15.13 gives us the least-squares line for predicting heart disease deaths per 100,000 people from liters of alcohol from wine consumed, per person. The line is based on data
The declining farm population. The number of people living on American farms has declined steadily during this century. Here are data on the farm population (millions of persons) from 1935 to
Going to class helps. A study of class attendance and grades among first-year students at a state university showed that in general students who attended a higher percentage of their classes earned
Always plot your data! Table 15.2 presents four sets of data prepared by the statistician Frank Anscombe to illustrate the dangers of calculating without first plotting the data. All four sets have
More on correlation and regression. In Exercises 15.6 and 15.8, the correlation and the slope of the least-squares line for IQ and school GPA are both positive. In Exercises 15.10 and 15.13, both the
Review of straight lines. During the period after birth, a male white rat gains exactly 40 grams (g) per week. (This rat is unusually regular in his growth, but 40 g per week is a realistic rate.)(a)
Review of straight lines. Fred keeps his savings in his mattress. He began with $1000 from his mother and adds $200 each year. His total savings y after x years are given by the equation y = 1000 +
Acid rain. Researchers studying acid rain measured the acidity of precipitation in a Colorado wilderness area for 150 consecutive weeks. Acidity is measured by pH. Lower pH values show higher
Correlation and regression. If the correlation between two variables x and y is r = 0, there is no straight-line relationship between the variables. It turns out that the correlation is 0 exactly
Wine and heart disease. In Exercises 15.10 and 15.13, you examined data on wine consumption and heart disease deaths from Table 15.1. Suggest some differences among nations that may be confounded
Strong association but no correlation. Exercise 14.19 (page 305)gives these data on the speed (miles per hour) and mileage (miles per gallon)of a car:Speed: 30 40 50 60 70 Mileage: 20 24 26 24 20 The
Wine and heart disease. Table 15.1 gives data on wine consumption and heart disease death rates in 19 countries in 2001. A scatterplot (Exercise 15.10) shows a moderately strong relationship. The
Beavers and beetles. Ecologists sometimes find rather strange relationships in our environment. One study seems to show that beavers benefit beetles. The researchers laid out 23 circular plots, each
Wine and heart disease. Drinking moderate amounts of wine may help prevent heart attacks. Let’s look at data for entire nations. Table 15.1 gives data on yearly wine consumption (liters of alcohol
The professor swims. Here are Professor Moore’s times (in minutes) to swim 2000 yards and his pulse rate (in beats per minute) after swimming for 23 sessions in the pool:Time: 34.12 35.72 34.72
IQ and school GPA. The least-squares line for predicting school GPA from IQ score, based on the 78 students plotted in Figure 14.10(page 302), is GPA = −3.56 + (0.101 × IQ)Explain in words the
State SAT scores. The correlation between the average SAT Mathematics score in the states and the proportion of high school seniors who take the SAT is r = −0.85.(a) The correlation is negative.
IQ and school GPA. Figure 14.10 (page 302) plots school grade point average (GPA) against IQ test score for 78 seventh-grade students. There is a roughly straight-line pattern with quite a bit of
State SAT scores. Figure 14.9 (page 301) plots the average SAT Mathematics score of each state’s high school seniors against the proportion of each state’s seniors who took the exam. In addition
Obesity in mothers and daughters. The study in Example 7 found that the correlation between the body mass index of young girls and their hours of physical activity in a day was r = −0.18. Why might
At the ballpark. Table 14.2 (page 307) gives data on the prices charged for a 16-ounce soda and for a hot dog at Major League Baseball stadiums. The correlation between the prices is r = 0.51.Do you
At the ballpark. Table 14.2(page 307) gives data on the prices charged for a 16-ounce soda and for a hot dog at Major League Baseball stadiums. The correlation between the prices is r = 0.51. What
Fossil bones. Use the equation of the least-squares line humerus length = −3.66 + (1.197 × femur length)to predict the humerus length for a fossil with a femur 70 cm long.
Now that we’ve covered nested models and interaction models, it’s important to understand which kinds of scenarios will lead you to which kinds of models. Below are several scenarios. For each
How does education affect how much people put trust in strangers, and does this vary by country type? Using the WVS dataset, run a regression equation using TRUST as the dependent variable, and three
Religiosity affects attitude toward divorce: the more religious a country, the less support for divorce. Does this relationship vary by country set? Using the WVS dataset, run a regression equation

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