AP Statistics Chapter 2

A company conducts an experiment in which a subject takes 50 mg of a substance orally. The researchers measure how many seconds it takes for the substance to exit the bloodstream. What kind of variable is the company studying?

quantitative variable.

A researcher measures the increase in heart rate of patients under a stress test. What kind of variable is the researcher studying?

quantitative variable.

Name the variables, and specify for each variable whether its use indicates that it should be treated as categorical or quantitative. Scientists at a major pharmaceutical firm conducted an experiment to study the effectiveness of an herbal compound to treat the common cold. They exposed each patient to a cold virus, then gave them either the herbal compound or a sugar solution known to have no effect on colds. Several days later they assessed each patient's condition, using a cold severity scale ranging from 0 to 5. They found no evidence of the benefits of the compound.

There are 2 variables. Categorical variable - type of treatment (herbal or sugar solution). Quantitative variable - severity rating.

Name the variables, and specify for each variable whether its use indicates that it should be treated as categorical or quantitative. A listing posted by the Arby's restaurant chain gives, for each of the sandwiches it sells, the type of meat in the sandwich, the number of calories, and the serving size in ounces. The data might be used to assess the nutritional value of the different sandwiches.

There are 3 variables. Quantitative variables - number of calories and serving size. Categorical variable - type of meat.

Name the variables, and specify for each variable whether its use indicates that it should be treated as categorical or quantitative. The Gallup Poll conducted a representative telephone survey of 1180 American voters during the first quarter of 2007. Among the reported results were the voter's region (Northeast, South, etc.), age, party affiliation, and whether or not the person had voted in the 2006 midterm congressional election.

There are 4 variables. Categorical variables - region, political affiliation, and whether or not the person voted in 1998. Quantitative variable - age.

Name the variables, and specify for each variable whether its use indicates that it should be treated as categorical or quantitative. Because of the difficulty of weighing a bear in the woods, researchers caught and measured 54 bears, recording their weight, neck size, length, and sex. They hoped to find a way to estimate weight from the other, more easily determined quantities.

There are 4 variables. Quantitative variables - weight, neck size, and length. (No units are specified.) Categorical variable - sex.

Name the variables, and specify for each variable whether its use indicates that it should be treated as categorical or quantitative. In performing research for an ecology class, students at a college in upstate New York collect data on streams each year. They record a number of biological, chemical, and physical variables, including the stream name, the substrate of the stream (limestone, shale, or mixed), the acidity of the water (pH), the temperature (°C), and the BCI (a numerical measure of biological diversity).

There are 5 variables. Categorical variables - name and substrate of the stream. Quantitative variables - acidity, temperature, and BCI.

Name the variables, and specify for each variable whether its use indicates that it should be treated as categorical or quantitative. To see whether people naturally walk in circles in the absence of visual clues, a researcher tested 32 people on a football field. One at a time, they stood at the center of one goal line, were blindfolded, and then tried to walk to the other goal line. She recorded each individual's sex, height, handedness, the number of yards each was able to walk before going out of bounds, and whether each wandered off course to the left or the right. No one made it all the way to the far end of the field without crossing one of the sidelines.

There are 5 variables. Categorical variables - sex, handedness, and side of the field. Quantitative variables - height and number of yards walked.

Name the variables, and specify for each variable whether its use indicates that it should be treated as categorical or quantitative. The EPA tracks fuel economy of automobiles based on information from the manufacturers (Ford, Toyota, etc.). Among the data the agency collects are the manufacturer, vehicle type (car, SUV, etc.), weight, horsepower, and gas mileage (mpg) for city and highway driving.

There are 6 variables. Quantitative variables - city mileage, highway mileage, weight, and horsepower. Categorical variables - manufacturer and type of car.

Name the variables, and specify for each variable whether its use indicates that it should be treated as categorical or quantitative. In 2006, Consumer Reports published an article evaluating refrigerators. It listed 41 models, giving the brand, cost, size (cu ft), type (such as top freezer), estimated annual energy cost, an overall rating (good, excellent, etc.), and the repair history for that brand (percentage requiring repairs over the past 5 years).

There are 7 variables. Categorical variables - brand, type, and overall rating. Quantitative variables - cost, size, estimated energy cost, and repair history.

Name the variables, and specify for each variable whether its use indicates that it should be treated as categorical or quantitative. The State Education Department requires local school districts to keep these records on all students: age, race or ethnicity, days absent, current grade level, standardized test scores in reading and mathematics, and any disabilities or special educational needs.

There are 7 variables. Categorical variables - race or ethnicity, grade level, and disabilities/special needs. Quantitative variables - number of absences, age, reading test score, and math test score.

Name the variables, and specify for each variable whether its use indicates that it should be treated as categorical or quantitative. Medical researchers at a large city hospital investigating the impact of prenatal care on newborn health collected data from 882 births during 1998-2000. They kept track of the mother's age, the number of weeks the pregnancy lasted, the type of birth (cesarean, induced, natural), the level of prenatal care the mother had (none, minimal, adequate), the birth weight and sex of the baby, and whether the baby exhibited health problems (none, minor, major).

There are 7 variables. Quantitative variables - mother's age, length of pregnancy, and birth weight of baby. Categorical variables - type of birth, level of prenatal care, gender of baby, and baby's health problems.

Name the variables, and specify for each variable whether its use indicates that it should be treated as categorical or quantitative. Business analysts hoping to provide information helpful to American grape growers compiled these data about vineyards: size (acres), number of years in existence, state, varieties of grapes grown, average case price, gross sales, and percent profit.

There are 7 variables. Quantitative variables - size of vineyard, number of years in existence, average case price, gross sales, and percent profit. Categorical variables - state and variety of grapes grown.

Identify the W's. For any quantitative variable, identify the units in which it was measured (or note that they were not provided). In 2006, Consumer Reports published an article evaluating refrigerators. It listed 41 models, giving the brand, cost, size (cu ft), type (such as top freezer), estimated annual energy cost, an overall rating (good, excellent, etc.), and the repair history for that brand (percentage requiring repairs over the past 5 years).

Who - 41 refrigerators What - Brand, cost (probably in dollars), size (in cu. ft.), type, estimated annual energy cost (probably in dollars), overall rating, and repair history (in percent requiring repair over the past five years) When - 2006 Where - United States Why - The information was compiled to provide information to the readers of Consumer Reports. How - Not specified.

Identify the W's. For any quantitative variable, identify the units in which it was measured (or note that they were not provided). Because of the difficulty of weighing a bear in the woods, researchers caught and measured 54 bears, recording their weight, neck size, length, and sex. They hoped to find a way to estimate weight from the other, more easily determined quantities.

Who - 54 bears. What - Weight, neck size, length (no specified units), and sex. When - Not specified. Where - Not specified. Why - Since bears are difficult to weigh, the researchers hope to use the relationships between weight, neck size, length, and sex of bears to estimate the weight of bears, given the other, more observable features of the bear. How - Researchers collected data on 54 bears they were able to catch.

Identify the W's. For any quantitative variable, identify the units in which it was measured (or note that they were not provided). Medical researchers at a large city hospital investigating the impact of prenatal care on newborn health collected data from 882 births during 1998-2000. They kept track of the mother's age, the number of weeks the pregnancy lasted, the type of birth (cesarean, induced, natural), the level of prenatal care the mother had (none, minimal, adequate), the birth weight and sex of the baby, and whether the baby exhibited health problems (none, minor, major).

Who - 882 births What - Mother's age (in years), length of pregnancy (in weeks), type of birth (caesarean, induced, or natural), level of prenatal care (none, minimal, or adequate), birth weight of baby (unit of measurement not specified, but probably pounds and ounces), gender of baby (male or female), and baby's health problems (none, minor, major) When - 1998-2000 Where - Large city hospital Why - Researchers were investigating the impact of prenatal care on newborn health. How - It appears that they kept track of all births in the form of hospital records, although it is not specifically stated.

Identify the W's. For any quantitative variable, identify the units in which it was measured (or note that they were not provided). A listing posted by the Arby's restaurant chain gives, for each of the sandwiches it sells, the type of meat in the sandwich, the number of calories, and the serving size in ounces. The data might be used to assess the nutritional value of the different sandwiches.

Who - Arby's sandwiches. What - type of meat, number of calories (in calories), and serving size (in ounces). When - Not specified. Where - Arby's restaurants Why - These data might be used to assess the nutritional value of the different sandwiches. How - Information was gathered from each of the sandwiches on the menu at Arby's, resulting in a census.

Identify the W's. For any quantitative variable, identify the units in which it was measured (or note that they were not provided). The EPA tracks fuel economy of automobiles based on information from the manufacturers (Ford, Toyota, etc.). Among the data the agency collects are the manufacturer, vehicle type (car, SUV, etc.), weight, horsepower, and gas mileage (mpg) for city and highway driving.

Who - Every model of automobile in the United States. What - Vehicle manufacturer, vehicle type, weight (probably in pounds), horsepower (in horsepower), and gas mileage (in miles per gallon) for city and highway driving. When - This information is collected currently Where - United States Why - The EPA uses the information to track fuel economy of vehicles. How - The data is collected from the manufacturer of each model.

Identify the W's. For any quantitative variable, identify the units in which it was measured (or note that they were not provided). In performing research for an ecology class, students at a college in upstate New York collect data on streams each year. They record a number of biological, chemical, and physical variables, including the stream name, the substrate of the stream (limestone, shale, or mixed), the acidity of the water (pH), the temperature (°C), and the BCI (a numerical measure of biological diversity).

Who - Streams What - Name of stream, substrate of the stream (limestone, shale, or mixed), acidity of the water (measured in pH), temperature (in degrees Celsius), and BCI (unknown units) When - Not specified Where - Upstate New York Why - Research is conducted for an Ecology class. How - Not specified.

Identify the W's. For any quantitative variable, identify the units in which it was measured (or note that they were not provided). The State Education Department requires local school districts to keep these records on all students: age, race or ethnicity, days absent, current grade level, standardized test scores in reading and mathematics, and any disabilities or special educational needs.

Who - Students. What - Age (probably in years, though perhaps in years and months), race or ethnicity, number of absences, grade level, reading score, math score, and disabilities/special needs. When - This information must be kept current. Where - Not specified. Why - Keeping this information is a state requirement. How - The information is collected and stored as part of school records.

Identify the W's. For any quantitative variable, identify the units in which it was measured (or note that they were not provided). Business analysts hoping to provide information helpful to American grape growers compiled these data about vineyards: size (acres), number of years in existence, state, varieties of grapes grown, average case price, gross sales, and percent profit.

Who - Vineyards What - Size of vineyard (in acres), number of years in existence, state, varieties of grapes grown, average case price (in dollars), gross sales (probably in dollars), and percent profit. When - Not specified. Where - United States Why - Business analysts hoped to provide information that would be helpful to producers of American wines. How - Not specified.

Identify Who and What were investigated and the population of interest. Researchers alternately taped two posters over a coffee station in an office. During one week, it was a picture of flowers; during the other, it was a pair of staring eyes. They found that the average contribution was significantly higher when the eyes poster was up than when the flowers were there. Apparently, the mere feeling of being watched was enough to encourage people to behave more honestly.

Who - Workers who buy coffee in an office What - amount of money contributed to the collection tray Population of interest - All people in honor system payment situations.

Identify the W's. For any quantitative variable, identify the units in which it was measured (or note that they were not provided). Scientists at a major pharmaceutical firm conducted an experiment to study the effectiveness of an herbal compound to treat the common cold. They exposed each patient to a cold virus, then gave them either the herbal compound or a sugar solution known to have no effect on colds. Several days later they assessed each patient's condition, using a cold severity scale ranging from 0 to 5. They found no evidence of the benefits of the compound.

Who - experiment volunteers What - herbal cold remedy or sugar solution, and cold severity. When - Not specified. Where - Major pharmaceutical firm Why - Scientists were testing the efficacy of an herbal compound on the severity of the common cold. How - The scientists set up a controlled experiment.

Name the variables, and specify for each variable whether its use indicates that it should be treated as categorical or quantitative. In a study, a research team reports that plants in southern England are flowering earlier in the spring. Records of the first flowering dates for 385 species over a period of 47 years show that flowering has advanced an average of 15 days per decade, an indication of climate warming.

Quantitative variable - date of first flowering.

Identify Who and What were investigated and the population of interest. The Cleveland Casting Plant is a producer of iron automotive castings for a company. The company is interested in keeping the pouring temperature of the molten iron (in degrees Fahrenheit) close to the specified value of 2550 degrees. Cleveland Casting measured the pouring temperature for 10 randomly selected crankshafts.

Who - 10 crankshafts at Cleveland Casting. What - The pouring temperature (in degrees Farenheit) of molten iron. Population of interest - All crankshafts at Cleveland Casting

Identify the W's. For any quantitative variable, identify the units in which it was measured (or note that they were not provided). The Gallup Poll conducted a representative telephone survey of 1180 American voters during the first quarter of 2007. Among the reported results were the voter's region (Northeast, South, etc.), age, party affiliation, and whether or not the person had voted in the 2006 midterm congressional election.

Who - 1180 Americans. What - Region, age (in years), political affiliation, and whether or not the person voted in the 1998 midterm Congressional election. When - First quarter of 1999 Where - United States Why - The information was gathered for presentation in a Gallup public opinion poll. How - Phone Survey

Identify Who and What were investigated and the population of interest. The movie industry would like to know what makes a movie successful. Data from 120 first-run movies released in 2005 suggest that longer movies actually make less profit.

Who - 120 first-run movies from 2005 What - length and profit of the movie Population of interest - All first-run movies

Identify Who and What were investigated and the population of interest. A psychologist wondered whether drivers treat bicycle riders differently when they wear helmets. He rigged his bicycle with a sensor that could measure how close each car was that passed him. He then rode on alternating days with and without a helmet. Out of 2500 cars passing him, he found that when he wore his helmet, motorists passed 3.35 inches closer to him, on average, than when his head was bare.

Who - 2,500 cars. What - Distance from the bicycle to the passing car (in inches). Population of interest - All cars passing bicyclists

Identify Who and What were investigated and the population of interest. Are physically fit people less likely to die of cancer? An article reported results of a study that followed 25,892 men aged 30 to 87 for 10 years. The most physically fit men had a 55% lower risk of death from cancer than the least fit group.

Who - 25,892 men What - Fitness level and cause of death. It is not clear what categories were used for fitness level. Population of interest - All men.

Identify Who and What were investigated and the population of interest. One company, concerned with what it believed was a low employee participation rate in its 401(k) plan, sampled 30 other companies with similar plans and asked for their 401(k) participation rates.

Who - 30 similar companies What - 401(k) employee participation rates (in percent). Population of interest - All similar companies

Identify the W's. For any quantitative variable, identify the units in which it was measured (or note that they were not provided). To see whether people naturally walk in circles in the absence of visual clues, a researcher tested 32 people on a football field. One at a time, they stood at the center of one goal line, were blindfolded, and then tried to walk to the other goal line. She recorded each individual's sex, height, handedness, the number of yards each was able to walk before going out of bounds, and whether each wandered off course to the left or the right. No one made it all the way to the far end of the field without crossing one of the sidelines.

Who - 32 volunteers What - Sex, height, handedness, the number of yards walked before going out of bounds, and the side of the field on which the person walked out of bounds. When - Not specified Where - Not specified Why - The researcher was interested in whether people walk in circles when lost. How - Data were collected by observing the people on the field, as well as by measuring and asking the participants.

Identify the W's. For any quantitative variable, identify the units in which it was measured (or note that they were not provided). In a study, a research team reports that plants in southern England are flowering earlier in the spring. Records of the first flowering dates for 385 species over a period of 47 years show that flowering has advanced an average of 15 days per decade, an indication of climate warming.

Who - 385 species of flowers. What - Date of first flowering (in days). When - Not specified Where - Southern England. Why - The researchers believe that this indicates a warming of the overall climate. How - Not specified.

A poll question asked, "Do you consider yourself a Republican, a Democrat, or an Independent?" The possible responses were "Democrat", "Republican", "Independent", "Other", and "No Response". What kind of variable is the response?

categorical variable.

A poll question asked, "Do you think things have gotten better or gotten worse in this country in the last 10 years?" Possible answers were "Better", "Worse", "No Change", "Don't Know", and "No Response". What kind of variable is the response?

categorical variable.