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mathematics
statistics the art and science
Statistics Unlocking The Power Of Data 1st Edition Robin H. Lock, Patti Frazer Lock, Kari Lock Morgan, Eric F. Lock, Dennis F. Lock - Solutions
In the book Scorecasting, we learn that ‘‘Across 43 professional soccer leagues in 24 different countries spanning Europe, South America, Asia, Africa, Australia, and the United States (covering more than 66,000 games), the home field advantage [percent of games won by the home team] in soccer
A recent study shows that antibiotics added to animal feed to accelerate growth can become airborne. Some of these drugs can be toxic if inhaled and may increase the evolution of antibiotic-resistant bacteria. Scientists analyzed 20 samples of dust particles from animal farms. Tylosin, an
A 2012 survey examined cell phone ownership by US adults. The results of the survey are shown in Table 2.7.Cell Phone Owned...............FrequencyAndroid smartphone.................458iPhone smartphone...................437Blackberry smartphone ............141Cell phone not smartphone......924No
Scientists are working to train dogs to smell cancer, including early stage cancer that might not be detected with other means. In previous studies, dogs have been able to distinguish the smell of bladder cancer, lung cancer, and breast cancer. Now, it appears that a dog in Japan has been trained
In Data 2.1 on page 46, we introduce a study in which people were asked whether they agreed or disagreed with the statement that there is only one true love for each person. Is the level of a person€™s education related to the answer given, and if so, how? Table 2.8 gives a two-way table
The StudentSurvey dataset includes variables on gender and on whether or not the student smokes. Who smokes more: males or females? Table 2.9 shows a two-way table of these two variables.Table 2.9(a) Which gender has a higher percentage of smokers: males or females?(b) What is the proportion of
A disruption of a gene called DYXC1 on chromosome 15 for humans may be related to an increased risk of developing dyslexia. Researchers studied the gene in 109 people diagnosed with dyslexia and in a control group of 195 others who had no learning disorder. The DYXC1 break occurred in 10 of those
People who have a brush with death occasionally report experiencing a near-death experience, which includes the sensation of seeing a bright light or feeling separated from one’s body or sensing time speeding up or slowing down. Researchers interviewed 1595 people admitted to a hospital cardiac
A recent study examined the link between miscarriage and the use of painkillers during pregnancy. Scientists interviewed 1009 women soon after they got positive results from pregnancy tests about their use of painkillers around the time of conception or in the early weeks of pregnancy. The
If we have learned to solve problems by one method, we often have difficulty bringing new insight to similar problems. However, electrical stimulation of the brain appears to help subjects come up with fresh insight. In a recent experiment conducted at the University of Sydney in Australia, 40
The Bureau of Labor Statistics in the US tells us that, in 2010, the unemployment rate for high school graduates with no college degree is 9.7% while the unemployment rate for college graduates with a bachelor’s degree is only 5.2%. Find the difference in proportions of those unemployed between
Studies have concluded that smoking while pregnant can have negative consequences, but could smoking also negatively affect one€™s ability to become pregnant? A study collected data on 678 women who had gone off birth control with the intention of becoming pregnant. Smokers were defined
Students in the ACHA€“NCHA survey were asked €˜€˜Within the last 12 months, have you been in a relationship (meaning an intimate/coupled/partnered relationship) that was emotionally abusive?€ The results are given in Table 2.12.(a) What percent of all
Students in the ACHA€“NCHA survey were asked €˜€˜Within the last two weeks, how many times have you had five or more drinks of alcohol at a sitting?€ The results are given inTable 2.13.(a) What percent of all respondents answered zero?(b) Of the students who
Students in the ACHA€“NCHA survey were asked two questions about alcohol use, one about their own personal consumption of alcohol and one about their perception of other students€™ consumption of alcohol. Figure 2.3(a) shows side-by-side bar charts for responses to the question
Students in the ACHA€“NCHA survey were asked €˜€˜Within the last 12 months, has stress negatively affected your academics?€ Figure 2.4(a) shows a segmented bar chart for response frequencies while Figure 2.4(b) shows a segmented bar chart for response
In order for a vaccine to be effective, it should reduce a person’s chance of acquiring a disease. Consider a hypothetical vaccine for malaria—a tropical disease that kills between 1.5 and 2.7 million people every year. Suppose the vaccine is tested with 500 volunteers in a village who are
Four students were working together on a project and one of the parts involved making a graph to display the relationship in a two-way table of data with two categorical variables: college accept/reject decision and type of high school (public, private, parochial). The graphs submitted by each
Which histograms are skewed to the left?Refer to histograms A through H in Figure 2.12. 2.0 -50 0.0 1.0 3 150 5 15 25 D -1 -3 8 14 -7 -4 -1 G Н Figure 2.12 Eight histograms LO 09 007 01 08 01 250 09 001 00€ 001
Which histograms are skewed to the right?Refer to histograms A through H in Figure 2.12. 2.0 -50 0.0 1.0 3 150 5 15 25 D -1 -3 8 14 -7 -4 -1 G Н Figure 2.12 Eight histograms LO 09 007 01 08 01 250 09 001 00€ 001
Which histograms are approximately symmetric?Refer to histograms A through H in Figure 2.12. 2.0 -50 0.0 1.0 3 150 5 15 25 D -1 -3 8 14 -7 -4 -1 G Н Figure 2.12 Eight histograms LO 09 007 01 08 01 250 09 001 00€ 001
Which histograms are approximately symmetric and bell-shaped?Refer to histograms A through H in Figure 2.12. 2.0 -50 0.0 1.0 3 150 5 15 25 D -1 -3 8 14 -7 -4 -1 G Н Figure 2.12 Eight histograms LO 09 007 01 08 01 250 09 001 00€ 001
For each of the four histograms A, B, C, and D, state whether the mean is likely to be larger than the median, smaller than the median, or approximately equal to the median.Refer to histograms A through H in Figure 2.12. 2.0 -50 0.0 1.0 3 150 5 15 25 D -1 -3 8 14 -7 -4 -1 G Н Figure 2.12 Eight
For each of the four histograms E, F, G, and H, state whether the mean is likely to be larger than the median, smaller than the median, or approximately equal to the median.Refer to histograms A through H in Figure 2.12. 2.0 -50 0.0 1.0 3 150 5 15 25 D -1 -3 8 14 -7 -4 -1 G Н Figure 2.12 Eight
Which of the distributions is likely to have the largest mean? The smallest mean?Refer to histograms A through H in Figure 2.12. 2.0 -50 0.0 1.0 3 150 5 15 25 D -1 -3 8 14 -7 -4 -1 G Н Figure 2.12 Eight histograms LO 09 007 01 08 01 250 09 001 00€ 001
Following the steps below, design a randomized comparative experiment to test whether fluoxetine (the active ingredient in Prozac pills) is effective at reducing depression. The participants are 50 people suffering from depression and the response variable is the change on a standard questionnaire
New research supports the idea that people who get a good night’s sleep look more attractive. In the study, subjects ages 18 to 31 were photographed twice, once after a good night’s sleep and once after being kept awake for 31 hours. Hair, make-up, clothing, and lighting were the same for both
A study published in 2010 showed that city dwellers have a 21% higher risk of developing anxiety disorders and a 39% higher risk of developing mood disorders than those who live in the country. A follow-up study published in 2011 used brain scans of city dwellers and country dwellers as they took a
A recent study examined the impact of the color red on how attractive men perceive women to be. In the study, men were randomly divided into two groups and were asked to rate the attractiveness of women on a scale of 1 (not at all attractive) to 9 (extremely attractive). One group of men were shown
In 2008, a study was conducted measuring the impact that music volume has on beer consumption. The researchers went into bars, controlled the music volume, and measured how much beer was consumed. The article states that ‘‘the sound level of the environmental music was manipulated according to
The president of a large university recently announced that the school would be switching to dorms that are all single-sex, because, he says, research shows that single-sex dorms reduce the number of student hook-ups for casual sex. He cites studies showing that, in universities that offer both
A headline at MSNBC.com stated ‘‘One way to ward off Alzheimer’s: Take a hike. Study: Walking at least one mile a day reduces risk of cognitive impairment by half.” The article reports on a study showing that elderly people who walked a lot tended to have more brain mass after nine years
In elementary school (grades 1 to 6), there is a strong association between a child’s height and the child’s reading ability. Taller children tend to be able to read at a higher level. However, there is a very significant confounding variable that is influencing both height and reading ability.
Three situations are described at the start of this section,. In the third bullet, we describe an association between the amount of salt spread on the roads and the number of accidents. Describe a possible confounding variable and explain how it fits the definition of a confounding variable.
Three situations are described at the start of this section. In the second bullet, we describe an association between activity at a building’s heating plant and more employees missing work due to back pain. A confounding variable in this case is amount of snow. Describe how snowfall meets the
‘‘Are there human pheromones?” Introduced. Three studies are described; indicate whether each of them is an experiment or an observational study.We describe data collection methods. Indicate whether the data come from an experiment or an observational study.
‘‘Is there a sprinting gene?”We describe data collection methods. Indicate whether the data come from an experiment or an observational study.
To examine whether farm-grown salmon contain more omega-3 oils if water is more acidic, we collect samples of salmon and water from multiple fish farms to see if the two variables are related.We describe data collection methods to answer a question of interest. Are we describing an experiment or an
To examine whether planting trees reduces air pollution, we find a sample of city blocks with similar levels of air pollution and we then plant trees in half of the blocks in the sample. After waiting an appropriate amount of time, we measure air pollution levels.We describe data collection methods
To examine whether playing music in a store increases the amount customers spend, we randomly assign some stores to play music and some to stay silent and compare the average amount spent by customers.We describe data collection methods to answer a question of interest. Are we describing an
To examine whether eating brown rice affects metabolism, we ask a random sample of people whether they eat brown rice and we also measure their metabolism rate.We describe data collection methods to answer a question of interest. Are we describing an experiment or an observational study?
People with shorter hair tend to be taller.Describe an association between two variables. Give a confounding variable that may help to account for this association.
Air pollution is higher in places with a higher proportion of paved ground relative to grassy ground.Describe an association between two variables. Give a confounding variable that may help to account for this association.
Sales of toboggans tend to be higher when sales of mittens are higher.Describe an association between two variables. Give a confounding variable that may help to account for this association.
People who own a yacht are more likely to buy a sports car.Describe an association between two variables. Give a confounding variable that may help to account for this association.
The total amount of beef consumed and the total amount of pork consumed worldwide are closely related over the past 100 years.Describe an association between two variables. Give a confounding variable that may help to account for this association.
More ice cream sales have been linked to more deaths by drowning.Describe an association between two variables. Give a confounding variable that may help to account for this association.
Want to lose weight? Eat more fiber!We give a headline that recently appeared online or in print. State whether the claim is one of association and causation, association only, or neither association nor causation.
Cat owners tend to be more educated than dog owners.We give a headline that recently appeared online or in print. State whether the claim is one of association and causation, association only, or neither association nor causation.
Wealthy people are more likely than other folks to lie, cheat, and steal.We give a headline that recently appeared online or in print. State whether the claim is one of association and causation, association only, or neither association nor causation.
Cell phone radiation leads to deaths in honey bees.We give a headline that recently appeared online or in print. State whether the claim is one of association and causation, association only, or neither association nor causation.
Among college students, no link found between number of friends on social networking websites and size of the university.We give a headline that recently appeared online or in print. State whether the claim is one of association and causation, association only, or neither association nor causation.
Daily exercise improves mental performance.We give a headline that recently appeared online or in print. State whether the claim is one of association and causation, association only, or neither association nor causation.
A strawberry farmer has planted 100 rows of plants, each 12 inches apart, and there are about 300 plants in each row. He would like to select a random sample of 30 plants to estimate the average number and weight of berries per plant.(a) Explain how he might choose the specific plants to include in
The Centers for Disease Control and Prevention (CDC) administers a large number of survey programs for monitoring the status of health and health care in the US. One of these programs is the National Health and Nutrition Examination Survey (NHANES), which interviews and examines a random sample of
Employment statistics in the US are often based on two nationwide monthly surveys: the Current Population Survey (CPS) and the Current Employment Statistics (CES) survey. The CPS samples approximately 60,000 US households and collects the employment status, job type, and demographic information of
Investigators posing as fair-skinned teenage girls contacted 300 tanning salons nationwide, including at least three randomly selected in each state. The investigators report that 90% of the salons stated that indoor tanning did not pose a health risk and over half (51%) of the salons denied that
The Pew Research Center polled a random sample of n = 808 US residents between the ages of 18 and 34. Of those in the sample, 24% had moved back in with their parents for economic reasons after living on their own. Do you think that this sample of 808 people is a representative sample of all US
In 1986 the Federal Office of Road Safety in Australia conducted an experiment to assess the effects of alcohol and marijuana on mood and performance. Participants were volunteers who responded to advertisements for the study on two rock radio stations in Sydney. Each volunteer was given a randomly
One of the daily polls on CNN.com during June 2011 asked ‘‘Does Physical Beauty Matter to You?” Of 38,485 people responding, 79% said yes and 21% said no. Can we conclude that about 79% of all people think physical beauty matters? Why or why not? In making such a conclusion, what are we
In a sample survey of professors at the University of Nebraska, 94% of them described themselves as ‘‘above average” teachers.(a) What is the sample? What is the population?(b) Based on the information provided, can we conclude that the study suffers from sampling bias?(c) Is 94% a good
In Example 1.10, we introduce a study by researchers from Harris Interactive who were interested in determining what percent of people wash their hands after using the washroom. They collected data by standing in public restrooms and pretending to comb their hair or put on make-up as they observed
Ask a random sample of students at the library on a Friday night ‘‘How many hours a week do you study?” to collect data to estimate the average number of hours a week that all college students study.Indicate whether we should trust the results of the study. Is the method of data collection
The population is adults between the ages of 18 and 22. A sample of 100 students is collected from a local university, and each student at the university had an equal chance of being selected for the sample.State whether or not the sampling method described produces a random sample from the given
The population is all employees at a company. All employees are emailed a link to a survey.State whether or not the sampling method described produces a random sample from the given population.
To estimate size of trout in a lake, an angler records the weight of 12 trout he catches over a weekend.State whether the data are best described as a population or a sample.
A large restaurant chain (see Example 1.6) periodically offers special milk shake flavors for a limited time. Suppose that the contenders for the next special flavor are Green Mint, Orange Crush, Egg Nog, and Pi ˜ na Colada. The chain plans to collect data from customers on these flavors, and
Take a random sample of one type of printer and test each printer to see how many pages of text each will print before the ink runs out. Use the average from the sample to estimate how many pages, on average, all printers of this type will last before the ink runs out.Indicate whether we should
Take 10 apples off the top of a truckload of apples and measure the amount of bruising on those apples to estimate how much bruising there is, on average, in the whole truckload.Indicate whether we should trust the results of the study. Is the method of data collection biased? If it is, explain why.
Ask a random sample of people in a given school district ‘‘Excellent teachers are essential to the well-being of children in this community, and teachers truly deserve a salary raise this year. Do you agree?” Use the results to estimate the proportion of all people in the school district who
The population is all people who visit the website CNN.com. All visitors to the website are invited to take part in the daily online poll.State whether or not the sampling method described produces a random sample from the given population.
The population is all trees in a forest. We walk through the forest and pick out trees that appear to be representative of all the trees in the forest.State whether or not the sampling method described produces a random sample from the given population.
The population is the approximately 25,000 protein-coding genes in human DNA. Each gene is assigned a number (from 1 to 25,000), and computer software is used to randomly select 100 of these numbers yielding a sample of 100 genes.State whether or not the sampling method described produces a random
The population is incoming students at a particular university. The name of each incoming student is thrown into a hat, the names are mixed, and 20 names (each corresponding to a different student) are drawn from the hat.State whether or not the sampling method described produces a random sample
To determine the height distribution of female high school students, the rosters are collected from 20 randomly selected high school girls basketball teams.(a) The sample.(b) The population of interest.(c) A population we can generalize to given the sample.
To investigate interest across all residents of the US in a new type of ice skate, a random sample of 1500 people in Minnesota are asked about their interest in the product.(a) The sample.(b) The population of interest.(c) A population we can generalize to given the sample.
To investigate the growth of the canine population in New York City, 100 dogs are randomly selected from a registry of licensed pets in the city, and it is found that 78 of them have been neutered.(a) The sample.(b) The population of interest.(c) A population we can generalize to given the sample.
To estimate the proportion of Americans who support changing the drinking age from 21 to 18, a random sample of 100 college students are asked the question ‘‘Would you support a measure to lower the drinking age from 21 to 18?”(a) The sample(b) The population of interest(c) A population we
The Nielsen Corporation attaches databoxes to televisions in 1000 households throughout the US to monitor what shows are being watched and produce the Nielsen Ratings for television.Describe the sample and describe a reasonable population.
A hungry yet diligent snacker eats an entire package of Chips Ahoy! cookies while counting and recording the number of chocolate chips in each cookie.Describe the sample and describe a reasonable population.
A cell phone carrier sends a satisfaction survey to 100 randomly selected customers.Describe the sample and describe a reasonable population.
Five hundred Canadian adults are asked if they are proficient on a musical instrument.Describe the sample and describe a reasonable population.
A fishing boat captain examines one day’s catch of fish to see if the average weight of fish in that area is large enough to make fishing there profitable.Describe the sample and describe a reasonable population.
A sociologist conducting a survey at a mall interviews 120 people about their cell phone use.Describe the sample and describe a reasonable population.
A questionnaire to understand athletic participation on a college campus is emailed to 50 college students, and all of them respond.State whether the data are best described as a population or a sample.
Are richer people happier? How might we collect data to answer this question? What would the cases be? What would the variable(s) be?
Suppose that we want to investigate the question ‘‘Does voter turnout differ by political party?” How might we collect data to answer this question? What would the cases be? What would the variable(s) be?
Forty-one employees of a biotechnology company participated in a study that examines the immunological and psychological effects of meditation. Twenty-five of the participants, chosen at random, completed an eight-week meditation program while the other 16 employees did no meditation. Brain wave
An economist collects data from many people to determine how age and income are related. How the data is collected determines whether the variables are quantitative or categorical. Describe how the information might be recorded if we regard both variables as quantitative. Then describe a different
On January 14, 2012, Andrew Brown of Great Britain set the world record time (40 days) for rowing solo across the northern Atlantic Ocean. On March 14, 2010, Katie Spotz of the United States became the youngest person to ever row solo across the Atlantic when she completed it in 70 days at the age
Hookahs are waterpipes used for smoking flavored tobacco. One study of 3770 university students in North Carolina found that 40% had smoked a hookah at least once, with many claiming that hookah smoke is safer than cigarette smoke. However, a second study observed people at a hookah bar and
In Exercise 1.17, we ask whether experiences of parents can affect future children, and describe a study that suggests the answer is yes. A second study, described in the same reference, shows similar effects. Young female mice were assigned to either live for two weeks in an enriched environment
Can experiences of parents affect future children? New studies suggest that they can: Early life experiences of parents appear to cause permanent changes in sperm and eggs. In one study, some male rats were fed a high-fat diet with 43% of calories from fat (a typical American diet), while others
Example 1.5 studied a variant of the gene ACTN3 which inhibits fast-twitch muscles and seems to be less prevalent in sprinters. A separate study indicated ethnic differences: Approximately 20% of a sample of Caucasians, approximately 25% of a sample of Asians, and approximately 1% of a sample of
When women take birth control pills, some of the hormones found in the pills eventually make their way into lakes and waterways. In one study, a water sample was taken from various lakes. The data indicate that as the concentration of estrogen in the lake water goes up, the fertility level of fish
Spiders regularly engage in spider foreplay that does not culminate in mating. Male spiders mature faster than female spiders and often practice the mating routine on not-yet-mature females. Since male spiders run the risk of getting eaten by female spiders, biologists wondered why spiders engage
The data from a study examining the association between diet and plasma retinol and beta-carotene levels are given in Nutrition Study. The data include 315 observations and 16 variables that are described in Appendix B.(a) Indicate which of the variables are quantitative and which are
Information about the world’s countries is given in All Countries, introduced in Data 1.2 . You can find a description of the variables in Appendix B. For the full dataset:(a) Indicate which of the variables are quantitative and which are categorical.(b) List at least two questions we might ask
Data 1.1 introduced the dataset StudentSurvey, and Example 1.2 identified seven of the variables in that dataset as categorical or quantitative. The remaining variables are:Year .........................................FirstYear, Sophomore, Junior, SeniorHeight
Year and the world record time in a marathon.A relationship between two variables is described. In each case, we can think of one variable as helping to explain the other. Identify the explanatory variable and the response variable.
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