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essential statistics
Statistics And Probability With Applications 3rd Edition Daren S. Starnes, Josh Tabor - Solutions
Exercise and memory A study of strength training and memory randomly assigned 46 young adults to two groups. After both groups were shown 90 pictures, one group had to bend and extend one leg against heavy resistance 60 times. The other group stayed relaxed, while the researchers used the same
Church and long life One of the better studies of the pg 246| effect of regular attendance at religious services gathered data from a random sample of 3617 adults. The researchers then measured many variables, not just the explanatory variable (religious activities) and the response variable
Sugar and gum disease The National Health and Nutrition Examination Survey is a long-term research program that uses random sampling methods to examine the health and nutrition among adults and children in the United States. One study of 2400 young adults found that subjects who consumed sugary
Batteries on ice Will storing batteries in a freezer make them last longer? A company that produces batteries takes a random sample of 100 AA batteries from its warehouse.The company statistician randomly assigns 50 batteries to be stored in the freezer and the other 50 to be stored at room
Age of Facebook users (2.1) Is there a relationship between Facebook use and age among college students?The following two-way table displays data for the 219 students who responded to a survey.
Voice vote (3.2) On the popular reality-TV show The Voice, viewers can vote for their favorite contestant by calling a toll-free number, by voting online, by texting, by using a smartphone app, or by purchasing a song on iTunes. The online rules describe the following restriction:“In each voting
Natural” experiment? A recent study compared the rate of crashes involving 16- to 18-year-old drivers in two adjacent Virginia counties. For two consecutive years, there were more crashes per person for drivers in this age group in Chesterfield County, where school starts at 7:20 A.M. , than in
Random headache relief In Exercise 4 , you described how to use slips of paper and a random number generator to randomly assign 36 subjects to one of four treatments:(1) antidepressant alone, (2) placebo alone, (3)antidepressant plus stress management, and (4) placebo plus stress management.
The power of milk? An article from the Arizona Daily Star tells the story of a gym trainer in London who swears by the power of milk to help him recover from workouts. The article describes how milk includes many of the same ingredients as sports drinks, as well as other proteins that help rebuild
Comparing treatments A large study used records from Canada’s national health care system to compare the effectiveness of two ways to treat prostate disease. The two treatments are traditional surgery and a new method that does not require surgery. The records described many cases where doctors
Building strength A high school football coach hears that a new exercise program will increase upperbody strength better than lifting weights. In the offseason, the coach lets his players choose which of the two treatments they will undergo for 3 weeks—exercise or weight lifting.He will use the
The future of preschool Does preschool help low-income children stay in school and hold good jobs later in life? The Carolina Abecedarian Project (the name suggests the ABCs) has followed a group of 111 children since 1972.Back then, these individuals were all healthy, low-income black infants in
Which diets work? Dr. Linda Stern and her colleagues recruited 132 obese adults at the Philadelphia Veterans Affairs Medical Center in Pennsylvania. Half the participants were randomly assigned to a lowcarbohydrate diet and the other half to a low-fat diet.Researchers measured each participant’s
Radishes and light Mr. Mills’s biology class conducted an experiment to investigate the impact of different light regimens on the growth of radish plants. They randomly assigned 60 2-day-old plants in identical pots to three treatments. Twenty plants were exposed to artificial“grow-light”
An apple a day? In an experiment to determine how calories in beverages affect appetite, researchers randomly assigned volunteers to one of four treatments:150 calories of apple slices, 150 calories of applesauce, 150 calories of apple juice, and 150 calories of apple juice with added fiber.
Vitamin D and asthma Researchers randomly assigned 408 adults with persistent asthma to take one of two treatments: an inhaled medicine with a vitamin D supplement or the inhaled medicine with a placebo.Results : After seven months, the vitamin D users were no less likely to experience reduced air
Pay to play? Are politicians more available to people who donate money to their campaigns? Researchers had members of a political organization attempt to schedule an appointment with members of Congress to discuss the banning of a particular chemical. Callers were identified as either a “local
More headache relief Explain the purpose of the random assignment in the experiment described in Exercise 4 .
More layoffs Explain the purpose of the random assignment in the experiment described in Exercise 3 .
More power, more speech? Explain the purpose of the random assignment in the experiment described in Exercise 2 .
Even more pizza Explain the purpose of the random assignment in the experiment described in Exercise 1 .
Headaches compared Doctors identify “chronic tensiontype headaches” as headaches that occur almost daily for at least six months. Can antidepressant medications or stress-management training reduce the number and severity of these headaches? Are both together more effective than either alone?
Effects of layoffs Workers who survive a layoff of other employees at their location may suffer from “survivor guilt.” A study used as subjects 120 students who were offered an opportunity to earn extra course credit by doing proofreading. Each subject worked in the same cubicle as another
Power and speech Recent research suggests that people’s speech patterns are influenced by how much power they think they have in a particular negotiation. In one study, 161 college students were randomly assigned to two groups. The subjects in one group were told they had higher status or inside
Pricey pizza? The cost of a meal might affect how customers evaluate and appreciate food. To investigate, researchers worked with an Italian all-you-can-eat buffet to perform an experiment. A total of 139 subjects were randomly assigned to pay either $4 or $8 for the buffet and then asked to rate
The mystery of the missing grade (2.5, 2.6) In Professor Friedman’s economics course, the correlation between the students’ total scores before the final examination and their final examination scores is r = 0.6.The pre-exam totals for all students in the course have mean 280 and standard
Get fit! (2.3, 3.1) A college fitness center offers an exercise program for staff members who choose to participate. The program assesses each participant’s fitness using a treadmill test and also administers a personality questionnaire. There is a moderately strong positive correlation between
Apartment complexes You are planning a report on apartment living in a college town. You decide to select three apartment complexes at random for indepth interviews with residents. The list of all apartment complexes in the college town is shown below.
Can you trust the WWW? You want to ask a sample of high-school students the question “How much do you trust information about health that you find on the Internet—a great deal, somewhat, not much, or not at all?” You try out this and other questions on a pilot group of 5 students chosen from
Mostly on time? An airline claims that 95% of its flights arrive on time. To check this claim, an SRS of 25 flights was selected and only 22 were on time. Do these data provide convincing evidence that less than 95% of all of this airline’s flights arrive on time?
Who banks online? A bank wants to estimate the proportion of its checking account customers who prefer to deposit checks in their account using a smartphone rather than making deposits at the local branch bank.
How far from home? A college administrator wants to estimate the mean distance that students at a large community college live from campus. To find out, she obtains a list of all students from the registrar’s database.
Weekend birthdays Over the years, the percentage of births that are planned caesarian sections has been rising. Because doctors can schedule these deliveries, there might be more children born during the week and fewer born on the weekend than if births were uniformly distributed throughout the
More lefties? In the population of people in the United States, about 10% are left-handed. After bumping elbows at lunch with several left-handed students, Simon wondered if more than 10% of students at his school are left-handed. To investigate, he selected an SRS of 50 students and found 7
Kissing the right way According to a newspaper article,“Most people are kissing the ‘right way.’” That is, according to a study, the majority of couples prefer to tilt their heads to the right when kissing. In the study, a researcher observed a random sample of 124 kissing couples and found
Spinning heads When a fair coin is flipped, we all pg 198 know that the probability the coin lands on heads is 0.50.However, what if a coin is spun? Two Polish math professors and their students spun a Belgian euro coin 250 times. It landed heads 140 times. One of the professors concluded that the
Estimating a proportion During the political crisis in Ukraine in spring 2014, a national polling organization asked an SRS of 2066 Americans to locate Ukraine on a map of the world. The sample proportion who successfully located Ukraine was 0.166. 14 (a) Do you think that the proportion of all
Estimating a mean In an SRS of 100 calls to a customer service line, the mean time that callers were placed on hold was 12.5 minutes. (a) Do you think the mean time that all callers to the customer service line were placed on hold is 12.5 minutes? Explain. (b) Suppose the customer-service manager
Estimating slope In an SRS of n = 10 used Honda CR-Vs, the slope of the least-squares regression line relating y = asking price (in dollars) to x = age (in years) is b = -892. (a) Do you think that the slope of the least-squares regression line relating asking price to age for all used Honda CR-Vs
Estimating correlation In an SRS of n = 6 students from Washington High School, the correlation between arm span (in centimeters) and height (in centimeters) is r =0.928.
Sampling for genealogy The local genealogical society in Coles County, Illinois, has compiled records on all 55,914 gravestones in cemeteries in the county for the years 1825 to 1985. Historians plan to use these records to learn about African Americans in Coles County’s history. They first
Sampling pines To gather data on a 1200-acre pine forest in Louisiana, the U.S. Forest Service laid a grid of 1410 equally spaced circular plots over a map of the forest. The Forest Service wants to visit a sample of 10%of these plots.
Holiday hours The management company of a local mall with 21 stores plans to survey 3 of the stores to determine the hours they would like to stay open during the holiday season.
Spring break family-style The school newspaper is pg 195 planning an article on family-friendly places to stay over spring break at a nearby beach town. The editors intend to call 4 randomly chosen hotels to ask about their amenities for families with children. They have an alphabetized list of all
Tipping at a buffet Do customers who stay longer at buffets give larger tips? Charlotte, a statistics student who worked at an Asian buffet, decided to investigate this question for her second-semester project. While working as a hostess, she obtained a random sample of receipts, which included the
Crying for higher IQ? Refer to Exercise 6, Does the fact that r = 0.45 suggest that making an infant cry will increase his or her IQ later in life? Explain.
More points, more turnovers? Refer to Exercise 5 .Does the fact that r = 0.92 suggest that an increase in turnovers will cause NBA players to score more points?Explain.
Long courtship, long marriage? A psychologist who specializes in divorce counseling finds that among his patients there is a linear relationship between the number of years of courtship before marriage and the number of years the couple stays married. The correlation is r =0.76. Does this suggest
GPA linked to pencils? For their final statistics project, Jordynn and Angie surveyed a random sample of 50 students at their school. Each student in the survey reported his or her GPA and the number of pencils in his or her possession at the moment. The association between number of pencils and
A kettle of hawks One of nature’s patterns connects the percent of adult birds in a colony that return from the previous year and the number of new adults that join the colony. Research on 13 colonies of sparrowhawks shows a linear relationship between these two variables, with a correlation of r
It’s warmer down here There is a roughly linear relationship between the latitude of major American cities and the average temperature in July. The correlation for the 12 cities with the largest populations is r = −0.55.Interpret this value.
A snap of a rubber band on the sole of the foot caused the infants to cry. The researchers recorded the crying and measured its intensity by the number of peaks in the most active 20 seconds. The relationship between these variables is linear, with a correlation of r = 0.45. Interpret this value.
Oh, that smarts! Infants who cry easily may be more easily stimulated than others. This may be a sign of higher IQ. Child development researchers explored the relationship between the crying of infants 4 to 10 days old and their IQ test scores at age
Points and turnovers There is a linear relationship between the number of turnovers and the number of points scored for players in the 2013–2014 NBA season.The correlation for these data is r = 0.92. Interpret this value.
Are education and income related? (1.8) The boxplots compare the distributions of income for full-time workers between the ages of 25 and 64 with five levels of education, after eliminating the top 5% and bottom 5% of incomes in each category. Write a brief description of how the distribution of
Two-income couples (2.1) Has the number of twoincome couples changed over time? The segmented bar chart shows the employment arrangements of married couples with children under 18 in 1960 and in 2011.Use the graph to determine if there is an association between year and employment arrangement.
Lean body mass and energy We have data on the lean body mass and resting metabolic rate for 12 women and 7 men who are subjects in a study of dieting. Lean body mass, given in kilograms, is a person’s weight leaving out all fat. Metabolic rate is measured in calories burned per 24 hours. The
Lagging or not? For a long time, the South has lagged behind the rest of the United States in the performance of its schools. Efforts to improve education have reduced the gap. Does the South stand out if we look at state average SAT Math scores? The figure enhances the scatterplot in Exercise 9 ,
Melting snow Explain what it means if there is a positive association between the amount of snow in the Colorado mountains during winter and the volume of water in area rivers during the following summer.
Burning oil Explain what it means if there is a negative association between the amount of fuel oil that a furnace uses and the outside temperature.
Different strengths Draw two scatterplots with positive linear associations but different strengths.
Different forms Draw two scatterplots with strong positive associations but different forms.
High-protein beans Beans and other legumes are an excellent source of protein. The table gives data on the total protein and carbohydrate content of a one-half cup portion of cooked beans for 12 different varieties. Make a scatterplot of the relationship between protein and carbohydrate content for
Income and mortality What does a country’s income per person (measured in adjusted gross domestic product per person in dollars) tell us about the mortality rate for children under 5 years of age (per 1000 live births)? Here are the data for a random sample of 14 countries in a recent year. Make
Is it colder up there? Refer to Exercise 8, Describe the relationship between elevation and average January temperature for these Colorado towns.
Crazy coasters Refer to Exercise 7, Describe the relationship between the height and maximum speed of the roller coasters.
IQ and GPA, connected? The scatterplot shows the school grade point average (GPA) on a 12-point scale and the IQ score for all 78 seventh-grade students in a rural midwestern school. Describe the relationship.
State SAT stats The scatterplot shows the percent of high school graduates in each state who took the SAT and the state’s mean SAT Math score in a recent year.Describe the relationship.
How’s the weather up there? The table presents data on the elevation (in feet) and average January temperature(in degrees Fahrenheit) for 10 cities and towns in Colorado. Make a scatterplot to show the relationship between elevation and average temperature in January.
Coaster crazy Many people like to ride roller coasters.Amusement parks try to increase attendance by building exciting new coasters. The table displays data on several roller coasters that were opened in a recent year. Make a scatterplot to show the relationship between height and maximum speed.
How much to carry? Ninth-grade students at the Webb Schools go on a backpacking trip each fall. Students are divided into hiking groups of size 8 by selecting names from a hat. Before leaving, students and their backpacks are weighed. The data here are from a group of hikers that one of the authors
Fast drive to an empty tank? How does the fuel consumption of a car change as its speed increases? Here are data for a British Ford Escort.Speed is measured in kilometers per hour, and fuel consumption is measured in liters of gasoline used per 100 kilometers traveled. Make a scatterplot by hand to
Mixed communication The number of texts and the number of calls for cell-phone users.
Vitruvian man The arm span and the height of high school seniors.
This is corny The yield of corn in bushels per acre and the amount of rain in the growing season.
Studying stats? The amount of time studying for a statistics exam and the grade on the exam.
More money (1.7) Refer to Exercise 20. (a) Find and interpret the interquartile range for total family income of the 38. individuals in the Indiana sample. (b) Interpret the standard deviation for the total family income of the 38 individuals in the Indiana sample.
Making money (1.9) The parallel dotplots show the total family income of randomly chosen individuals from Indiana (38 individuals) and New Jersey (44 individuals).Means and standard deviations are given below the dotplots.
Mosaic plots A mosaic plot resembles a segmented bar chart except that the width of the bars corresponds to the proportion of individuals in each category of the explanatory variable. Here is an example of the mosaic plot for the Titanic data on page 98 . Following this example, make a mosaic plot
Reversing the variables In the Titanic example from this lesson, we learned that there was an association between the class of travel (explanatory variable) and the survival status (response variable) for passengers on the Titanic.Would there still be an association if the variables were reversed
Who owns a home? Using data from the 2010 census, a random sample of 348 U.S. residents aged 18 and older was selected. Among the variables recorded were gender(male or female), housing status (rent or own), and marital status (married or not married). The first two-way table summarizes the
More regional parties Refer to Exercise 14, Draw a segmented bar chart that would show no association between U.S. region and party affiliation for members of the House of Representatives.
More snowmobiles Refer to Exercise 13, Draw a segmented bar chart that would show no association between environmental club membership and snowmobile use for the members of the sample.
Regional parties The two-way table gives the party affiliation of all members of the House of Representatives from eight different regions in the United States in July 2014 (there were 3 vacant seats at that time)(a) Make a segmented bar chart to show the relationship between U.S. region and party
Green snowmobiles? Yellowstone National Park surveyed a random sample of 1526 winter visitors to the park. The survey asked each person if he or she owned, rented, or had never used a snowmobile. Respondents were also asked whether or not they belonged to an environmental organization (like the
How do you get to school? Random samples of high school students in Australia and New Zealand were asked how they typically get to school. The side-by-side bar chart summarizes the data. Based on the graph, is there an association between country and travel method for the members of the sample?
Color my world Favorite vehicle colors may differ among countries. The side-by-side bar chart shows data on the most popular colors of cars in a recent year for the United States and Europe. Based on the graph, is there an association between color preference and where you live?Explain your
Who buys Toyotas? The segmented bar chart summarizes the distribution of sales of Toyotas in different regions of the world. Use the graph to determine if there is an association between region and year. Explain your reasoning. If there is an association, briefly describe it.
Still on a land line? Telephone surveys made through random-digit dialing used to exclude cell-phone numbers.If the opinions of people who have only cell phones differ from those of people who have landline service, the poll results may not represent all adults. The Pew Research Center interviewed
Growing into algebra? At Springfield High School, there are freshman, sophomores, and juniors taking Algebra II.Ms. Fernandez, the chairman of the Mathematics Department, wonders if there is a relationship between year in school and performance in the course. Use the information in the two-way
Get rich quick A survey of 4826 randomly selected young adults (aged 19 to 25) asked, “What do you think the chances are you will have much more than a middle-class income at age 30?” The gender of each respondent was also recorded. Use the information in the two-way table to make a segmented
Warm cozy nests How is the hatching of water python eggs influenced by the temperature of the snake’s nest?Researchers assigned newly laid eggs to one of three water temperatures: hot, neutral, or cold. Hot duplicates the extra warmth provided by the mother python, and cold duplicates the absence
Cell-phone preferences The Pew Research Center asked a random sample of 2024 adult cell-phone owners from the United States their age and which type of cell phone they own: iPhone, Android, or other (including non-smart phones). Use the information in the two-way table to make a segmented bar chart
Are you graduating? Participation in extracurricular activities during high school and graduation status.
Everyone likes sports Gender and favorite sport?
Don’t smoke Whether or not a person develops lung cancer and smoking status.
Dorm life Residential status (on- or off-campus) and year in college.
Mrs. Causey asked her students how much time they had spent using a computer during the previous week. The following figure shows a cumulative relative frequency graph of her students’ responses.
During the early part of a Major League Baseball season, many fans and players noticed that the number of home runs being hit seemed unusually large. Here are the data on the number of home runs hit by American League and National League teams in the early part of that season:
The dotplots show the lifetimes of several Brand X and Brand Y batteries.
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