1. 1.1 What is statistics?

2. 1.2 Explain the difference between descriptive and inferential statistics.

3. 1.3 List and define the five elements of an inferential statistical analysis.

4. 1.4 List the four major methods of collecting data, and explain their differences.

5. 1.5 Explain the difference between quantitative and qualitative data.

6. 1.6 Explain how populations and variables differ.

7. 1.7 Explain how populations and samples differ.

8. 1.8 What is a representative sample? What is its value?

9. 1.9 Why would a statistician consider an inference incomplete without an accompanying measure of its reliability?

10. 1.10 Define statistical thinking.

11. 1.11 Suppose you’re given a data set that classifies each sample unit into one of four categories: A, B, C, or D. You plan to create a computer database consisting of these data, and you decide to code the data as $\mathrm{A}=1$, $\mathrm{B}=2$, $\mathrm{C}=3$, and $\mathrm{D}=4$. Are the data consisting of the classifications A, B, C, and D qualitative or quantitative? After the data are input as 1, 2, 3, or 4, are they qualitative or quantitative? Explain your answers.

The Random Numbers applet generates a list of n random numbers from 1 to N, where n is the size of the sample and N is the size of the population. The list generated often contains repetitions of one or more numbers.

1. Using the applet Random Numbers, enter 1 for the minimum value, 10 for the maximum value, and 10 for the number of samples. Then click on Sample. Look at the results, and list any numbers that are repeated and the number of times each of these numbers occurs.

2. Repeat part (a), changing the maximum value to 20 and keeping the size of the sample fixed at 10. If you still have repetitions, repeat the process, increasing the maximum value by 10 each time but keeping the size of the sample fixed. What is the smallest maximum value for which you had no repetitions?

3. Describe the relationship between the population size (maximum value) and the number of repetitions in the list of random numbers as the population size increases and the sample size remains the same. What can you conclude about using a random number generator to choose a relatively small sample from a large population?

The Random Numbers applet can be used to select a random sample from a population, but can it be used to simulate data? In parts (a) and (b), you will use the applet to create data sets. Then you will explore whether those data sets are realistic.

1. Consider the number of customers waiting in line to order at a fast-food outlet. Use the Random Numbers applet to simulate this data set by setting the minimum value equal to 0, the maximum value equal to 99, and the sample size equal to 30. Explain what the numbers in the list produced by the applet represent in the context of the problem. Do the numbers produced by the applet seem reasonable? Explain.

2. Use the Random Numbers applet to simulate grades on a statistics test by setting the minimum value equal to 0, the maximum value equal to 100, and the sample size equal to 30. Explain what the numbers in the list produced by the applet represent in this context. Do the numbers produced by the applet seem reasonable? Explain.

3. Referring to parts (a) and (b), why do the randomly generated data seem more reasonable in one situation than in the other? Comment on the usefulness of using a random-number generator to produce data.

1. 1.12 College application. Colleges and universities are requiring an increasing amount of information about applicants before making acceptance and financial aid decisions. Classify each of the following types of data required on a college application as quantitative or qualitative.

   1. High school GPA

   2. High school class rank

   3. Applicant’s score on the SAT or ACT

   4. Gender of applicant

   5. Parents’ income

   6. Age of applicant

2. 1.13 STEM experiences for girls. The National Science Foundation (NSF) promotes girls’ participation in informal science, technology, engineering, and mathematics (STEM) programs. What has been the impact of these informal STEM experiences? This was the question of interest in the published study Cascading Influences: Long-Term Impacts of Informal STEM Experiences for Girls (Mar. 2013). A sample of 159 young women who recently participated in a STEM program were recruited to complete an online survey. Of these, only 27% felt that participation in the STEM program increased their interest in science.

   1. Identify the population of interest to the researchers.

   2. Identify the sample.

   3. Use the information in the study to make an inference about the relevant population.

3. 1.14 Drafting NFL quarterbacks. The Journal of Productivity Analysis (Vol. 35, 2011) published a study of how successful National Football League (NFL) teams are in drafting productive quarterbacks. Data were collected for all 331 quarterbacks drafted over a 38-year period. Several variables were measured for each QB, including draft position (one of the top 10 players picked, selection between picks 11–50, or selected after pick 50), NFL winning ratio (percentage of games won), and QB production score (higher scores indicate more productive QBs). The researchers discovered that draft position was only weakly related to a quarterback’s performance in the NFL. They concluded that “quarterbacks taken higher [in the draft] do not appear to perform any better.”

   1. What is the experimental unit for this study?

   2. Identify the type (quantitative or qualitative) of each variable measured.

   3. Is the study an application of descriptive or inferential statistics? Explain.

4. 1.15 Ground motion of earthquakes. In the Journal of Earthquake Engineering (Nov. 2004), a team of civil and environmental engineers studied the ground motion characteristics of 15 earthquakes that occurred around the world since 1940. Three (of many) variables measured on each earthquake were the type of ground motion (short, long, or forward directive), the magnitude of the earthquake (on the Richter scale), and peak ground acceleration (feet per second). One of the goals of the study was to estimate the inelastic spectra of any ground motion cycle.

   1. Identify the experimental units for this study.

   2. Do the data for the 15 earthquakes represent a population or a sample? Explain.

   3. Define the variables measured and classify them as quantitative or qualitative.

5. 1.16 Sprint speed training. The Sport Journal (Winter 2004) reported on a study of a speed-training program for high school football players. Each participant was timed in a 40-yard sprint both before and after training. The researchers measured two variables: (1) the difference between the before and after sprint times (in seconds), and (2) the category of improvement (“improved,” “no change,” and “worse”) for each player.

   1. a. Identify the type (quantitative or qualitative) of each variable measured.

   2. b. A total of 14 high school football players participated in the speed-training program. Does the data set collected represent a population or a sample? Explain.

6. 1.17 Corrosion prevention of buried steel structures. Engineers have designed tests on underground steel structures that measure the potential for corrosion. In Materials Performance (Mar. 2013), two tests for steel corrosion—called “instant-off” and “instant-on” potential—were compared. The tests were applied to buried piping at a petrochemical plant. Both the “instant-off” and “instant-on” corrosion measurements were made at each of 19 different randomly selected pipe locations. One objective of the study is to determine if one test is more desirable (i.e., can more accurately predict the potential for corrosion) than the other when applied to buried steel piping.

   1. What are the experimental units for this study?

   2. Describe the sample.

   3. Describe the population.

   4. Is this an example of descriptive or inferential statistics?

7. 1.18 Student GPAs. Consider the set of all students enrolled in your statistics course this term. Suppose you’re interested in learning about the current grade point averages (GPAs) of this group.

   1. Define the population and variable of interest.

   2. Is the variable qualitative or quantitative?

   3. Suppose you determine the GPA of every member of the class. Would this determination represent a census or a sample?

   4. Suppose you determine the GPA of 10 members of the class. Would this determination represent a census or a sample?

   5. If you determine the GPA of every member of the class and then calculate the average, how much reliability does your calculation have as an “estimate” of the class average GPA?

   6. If you determine the GPA of 10 members of the class and then calculate the average, will the number you get necessarily be the same as the average GPA for the whole class? On what factors would you expect the reliability of the estimate to depend?

   7. What must be true in order for the sample of 10 students you select from your class to be considered a random sample?

8. 1.19 Medicinal value of plants. Sea buckthorn (Hippophae), a plant that typically grows at high altitudes in Europe and Asia, has been found to have medicinal value. The medicinal properties of berries collected from sea buckthorn were investigated in Academia Journal of Medicinal Plants (Aug. 2013). The following variables were measured for each plant sampled. Identify each as producing quantitative or qualitative data.

   1. Species of sea buckthorn (H. rhamnoides, H. gyantsensis, H. neurocarpa, H. tibetana, or H. salicifolia)

   2. Altitude of collection location (meters)

   3. Total flavonoid content in berries (milligrams per gram)

9. 1.20 Extinct birds. Biologists at the University of California (Riverside) are studying the patterns of extinction in the New Zealand bird population. (Evolutionary Ecology Research, July 2003.) At the time of the Maori colonization of New Zealand (prior to European contact), the following variables were measured for each bird species:

   1. Flight capability (volant or flightless)

   2. Type of habitat (aquatic, ground terrestrial, or aerial terrestrial)

   3. Nesting site (ground, cavity within ground, tree, cavity above ground)

   4. Nest density (high or low)

   5. Diet (fish, vertebrates, vegetables, or invertebrates)

   6. Body mass (grams)

   7. Egg length (millimeters)

   8. Extinct status (extinct, absent from island, present)

   Identify each variable as quantitative or qualitative.

10. 1.21 Study of quality of drinking water. Disasters (Vol. 28, 2004) published a study of the effects of a tropical cyclone on the quality of drinking water on a remote Pacific island. Water samples (size 500 milliliters) were collected approximately four weeks after Cyclone Ami hit the island. The following variables were recorded for each water sample:

    1. Town where sample was collected

    2. Type of water supply (river intake, stream, or borehole)

    3. Acidic level (pH scale, 1 to 14)

    4. Turbidity level (nephalometric turbidity $\text{units}=\text{NTUs}$)

    5. Temperature (degrees centigrade)

    6. Number of fecal coliforms per 100 milliliters

    7. Free-chlorine residual (milligrams per liter)

    8. Presence of hydrogen sulphide (yes or no)

    Identify each variable as quantitative or qualitative.

1. 1.22 Annual survey of computer crimes. The Computer Security Institute (CSI) conducts an annual survey of computer crime at U.S. businesses. CSI sends survey questionnaires to computer security personnel at all U.S. corporations and government agencies. The latest CSI survey was sent by post or email to 5,412 firms, and 351 organizations responded. Forty-one percent of the respondents admitted unauthorized use of computer systems at their firms during the year. (CSI Computer Crime and Security Survey, 2010/2011.)

   1. Identify the population of interest to CSI.

   2. Identify the data collection method used by CSI. Are there any potential biases in the method used?

   3. Describe the variable measured in the CSI survey. Is it quantitative or qualitative?

   4. What inference can be made from the study result?

2. 1.23 Treasury deficit prior to the Civil War. In Civil War History (June 2009), historian Jane Flaherty researched the condition of the U.S. Treasury on the eve of the Civil War in 1861. Between 1854 and 1857 (under President Franklin Pierce), the annual surplus/deficit was $+18.8,+6.7,+5.3,$ and $+1.3\text{million}$ dollars, respectively. In contrast, between 1858 and 1861 (under President James Buchanan), the annual surplus/deficit was $-27.3,-16.2,-7.2,$ and $-25.2\text{million}$ dollars, respectively. Flaherty used these data to aid in portraying the exhausted condition of the U.S. Treasury when Abraham Lincoln took office in 1861. Does this study represent a descriptive or inferential statistical study? Explain.

3. 1.24 Satellite database. The Union for Concerned Scientists (UCS) maintains the Satellite Database—a listing of the more than 1,000 operational satellites currently in orbit around Earth. Several of the many variables stored in the database include country of operator/owner, primary use (civil, commercial, government, or military), class of orbit (low earth, medium earth, or geosynchronous), longitudinal position (degrees), apogee (i.e., altitude farthest from Earth’s center of mass in kilometers), launch mass (kilograms), usable electric power (watts), and expected lifetime (years). Which of the variables measured are qualitative? Which are quantitative?

4. 1.25 National Bridge Inventory. All highway bridges in the United States are inspected periodically for structural deficiency by the Federal Highway Administration (FHWA). Data from the FHWA inspections are compiled into the National Bridge Inventory (NBI). Several of the nearly 100 variables maintained by the NBI are listed next. Classify each variable as quantitative or qualitative.

   1. Length of maximum span (feet)

   2. Number of vehicle lanes

   3. Toll bridge (yes or no)

   4. Average daily traffic

   5. Condition of deck (good, fair, or poor)

   6. Bypass or detour length (miles)

   7. Type of route (interstate, U.S., state, county, or city)

5. 1.26 Corporate sustainability. Corporate sustainability refers to business practices designed around social and environmental considerations (e.g., “going green”). Business and Society (Mar. 2011) published a paper on how firm size and firm type affect sustainability behaviors. A survey was sent to approximately 23,500 senior managers at CPA firms, of which 1,293 senior managers responded. (Note: It is not clear how the 23,500 senior managers were selected.) Due to missing data (incomplete survey answers), only 992 surveys were analyzed. These data were used to infer whether larger firms are more likely to report sustainability policies than smaller firms and whether public firms are more likely to report sustainability policies than private firms.

   1. Identify the population of interest to the researchers.

   2. What method was used to collect the sample data?

   3. Comment on the representativeness of the sample.

   4. How will your answer to part c affect the validity of the inferences drawn from the study?

6. 1.27 CT scanning for lung cancer. A new type of screening for lung cancer, computed tomography (CT), has been developed. Medical researchers believe that CT scans are more sensitive than regular X-rays in pinpointing small tumors. The H. Lee Moffitt Cancer Center at the University of South Florida conducted a clinical trial of 50,000 smokers nationwide to compare the effectiveness of CT scans with X-rays for detecting lung cancer. (Todays’ Tomorrows, Fall 2002.) Each participating smoker was randomly assigned to one of two screening methods, CT or chest X-ray, and his or her progress tracked over time. The age at which the scanning method first detects a tumor is the variable of interest.

   1. Identify the data collection method used by the cancer researchers.

   2. Identify the experimental units of the study.

   3. Identify the type (quantitative or qualitative) of the variable measured.

   4. Identify the population and sample.

   5. What is the inference that will ultimately be drawn from the clinical trial?

7. 1.28 Zillow.com estimates of home values. Zillow.com is a real estate Web site that provides free estimates of the market value of homes. A trio of University of Texas at San Antonio professors compared Zillow estimates to actual sale prices of homes and published their results in The Appraisal Journal (Winter 2010). The analysis was based on data collected for 2,045 single-family residential properties in Arlington, Texas, that sold during a recent year. Sale price and Zillow estimated value (in dollars) were measured for each property. Zillow claims that this market has one of its highest accuracy ratings. However, the research revealed that Zillow overestimated the market value by more than 10% for nearly half of the properties.

   1. What is the experimental unit for this study?

   2. Describe the variables measured in the study. Do these variables produce quantitative or qualitative data?

   3. Give a scenario where the 2,045 properties represent a population.

   4. If the 2,045 properties represent a representative sample from a population, describe the population.

   5. Suppose the relevant population is all single-family residential properties in the United States. Do you believe the 2,045 properties are representative of this population? Explain.

8. 1.29 Massage vs. rest in boxing. Does a massage enable the muscles of tired athletes to recover from exertion faster than usual? To answer this question, researchers recruited eight amateur boxers to participate in an experiment. (British Journal of Sports Medicine, Apr. 2000.) After a 10-minute workout in which each boxer threw 400 punches, half the boxers were given a 20-minute massage and half just rested for 20 minutes. Before they returned to the ring for a second workout, the heart rate (beats per minute) and blood lactate level (micromoles) were recorded for each boxer. The researchers found no difference in the means of the two groups of boxers for either variable.

   1. Identify the data collection method used by the researchers.

   2. Identify the experimental units of the study.

   3. Identify the variables measured and their type (quantitative or qualitative).

   4. What is the inference drawn from the analysis?

   5. Comment on whether this inference can be made about all athletes.

9. 1.30 Insomnia and education. Is insomnia related to education status? Researchers at the Universities of Memphis, Alabama at Birmingham, and Tennessee investigated this question in the Journal of Abnormal Psychology (Feb. 2005). Adults living in Tennessee were selected to participate in the study, which used a random-digit telephone dialing procedure. Two of the many variables measured for each of the 575 study participants were number of years of education and insomnia status (normal sleeper or chronic insomniac). The researchers discovered that the fewer the years of education, the more likely the person was to have chronic insomnia.

   1. Identify the population and sample of interest to the researchers.

   2. Identify the data collection method. Are there any potential biases in the method used?

   3. Describe the variables measured in the study as quantitative or qualitative.

   4. What inference did the researchers make?

10. 1.31 Guilt in decision making. The effect of the emotion of guilt on how a decision maker focuses on a problem was investigated in the Journal of Behavioral Decision Making (January 2007). A total of 155 volunteer students participated in the experiement, where each was randomly assigned to one of three emotional states (guilt, anger, or neutral) through a reading/writing task. Immediately after the task, the students were presented with a decision problem (e.g., whether or not to spend money on repairing a very old car). The researchers found that a higher proportion of students in the guilty-state group chose not to repair the car than those in the neutral-state and anger-state groups.

    1. Identify the population, sample, and variables measured for this study.

    2. Identify the data collection method used.

    3. What inference was made by the researcher?

    4. In later chapters you will learn that the reliability of an inference is related to the size of the sample used. In addition to sample size, what factors might affect the reliability of the inference drawn in this study?

1. 1.32 Can money spent on gifts buy love? Is the gift you purchased for that special someone really appreciated? This was the question investigated in the Journal of Experimental Social Psychology (Vol. 45, 2009). The researchers examined the link between engagement ring price (dollars) and level of appreciation of the recipient (measured on a 7-point scale where $1=$“not at all” and $7=$“to a great extent”). Participants for the study were those who used a popular Web site for engaged couples. The Web site’s directory was searched for those with “average” American names (e.g., “John Smith,” “Sara Jones”). These individuals were then invited to participate in an online survey in exchange for a $10 gift certificate. Of the respondents, those who paid really high or really low prices for the ring were excluded, leaving a sample size of 33 respondents.

   1. Identify the experimental units for this study.

   2. What are the variables of interest? Are they quantitative or qualitative in nature?

   3. Describe the population of interest.

   4. Do you believe the sample of 33 respondents is representative of the population? Explain.

   5. In a second, designed study, the researchers investigated whether the link between gift price and level of appreciation was stronger for birthday gift givers than for birthday gift receivers. The participants were randomly assigned to play the role of gift-giver or gift-receiver. Assume that the sample consists of 50 individuals. Use a random number generator to randomly assign 25 individuals to play the gift-receiver role and 25 to play the gift-giver role.

2. 1.33 Dating and disclosure. As an adolescent, did you voluntarily disclose information about dating and romantic relationships to your parents? This was the research question of interest in the Journal of Adolescence (Apr. 2010). A sample of 222 high school students was recruited to participate in the study. Some of the many variables measured on each student were age (years), gender, dating experience (number of dates), and the extent to which the student was willing to tell his/her parent (without being asked) about a dating issue (e.g., how late the daters stayed out). The responses for the last variable were categorized as “never tell,” “rarely tell,” “sometimes tell,” “almost always tell,” and “always tell.”

   1. a. Identify the data type for each variable.

   2. b. The study was unclear on exactly how the sample of students was selected, stating only that “participants were recruited from health or government classes in a primarily European American middle-class school district.” Based on this information, what are the potential caveats to using the sample to make inferences on dating and disclosure to parents for all high school students?

3. 1.34 Jersey City drug market study. An article in the Journal of Quantitative Criminology (Mar. 2014) discussed several data collection methods for testing the efficacy of a new program designed to reduce drug-related crimes in Jersey City (N.J.). The sample consisted of 56 “hot spots”—areas of Jersey City with a high crime rate but not necessarily a high drug crime rate. In Method 1, the new program will be implemented in half of the 56 hot spots (selected at random); the other half will not implement the program (the “no treatment” group). In Method 2, the 56 hot spots will be divided into four groups based on the level of drug crimes—very high drug crime rate (10 hot spots), high rate (8 hot spots), moderate rate (26 hot spots), and low rate (12 hot spots). In each group, half the hot spots will be randomly assigned the new crime prevention program and the other half no treatment. For both methods, after several weeks the crime rates in the hot spots where the program was implemented will be compared with those with no treatment.

   1. Identify the data collection method for Method 1.

   2. Identify the data collection method for Method 2.

   3. Is this an application of descriptive or inferential statistics? Explain.

   4. Given that there is a great deal of variation in the drug crime rates at the 56 hot spots, which data collection method do you recommend? Explain.

1. 1.35 Your choice for a mom. After running stories on current First Lady Michelle Obama and former vice presidential candidate Sarah Palin on consecutive weeks, USA Weekend magazine asked its readers on Mother’s Day, “Who would you rather have as your mom, Sarah Palin or Michelle Obama?” Readers were asked to vote online at www.usaweekend.com. Based on over 34,000 votes cast, the results were: Obama—71%, Palin—29%. (USA Weekend Magazine press release, May 11, 2010.)

   1. a. What type of data collection method is used in this study?

   2. b. Is the data collected quantitative or qualitative? Explain.

   3. c. Discuss the validity of the study results. What are the potential problems with running a poll where voting is done online?

2. 1.36 20/20 survey exposés. Several years ago, the popular prime-time ABC television program 20/20 presented several misleading (and possibly unethical) surveys in a segment titled “Facts or Fiction? Exposés of So-Called Surveys.” The information reported from four of these surveys, conducted by businesses or special-interest groups with specific objectives in mind, is given. (Actual survey facts are provided in parentheses.)

   • Quaker Oats Study: Eating oat bran is a cheap and easy way to reduce your cholesterol count. (Fact: Diet must consist of nothing but oat bran to achieve a slightly lower cholesterol count.)

   • March of Dimes Report: Domestic violence causes more birth defects than all medical issues combined. (Fact: No study—false report.)

   • American Association of University Women (AAUW) study: Only 29% of high school girls are happy with themselves, compared with 66% of elementary school girls. (Fact: Of 3,000 high school girls, 29% responded “Always true” to the statement, “I am happy the way I am.” Most answered, “Sort of true” and “Sometimes true.”)

   • Food Research and Action Center study: One in four American children under age 12 is hungry or at risk of hunger. (Fact: Survey results are based on responses to the questions “Do you ever cut the size of meals?,” “Do you ever eat less than you feel you should?” and “Did you ever rely on limited numbers of foods to feed your children because you were running out of money to buy food for a meal?”)

   1. Refer to the Quaker Oats study relating oat bran to cholesterol levels. Discuss why it is unethical to report the results as stated.

   2. Consider the false March of Dimes report on domestic violence and birth defects. Discuss the type of data required to investigate the impact of domestic violence on birth defects. What data collection method would you recommend?

   3. Refer to the AAUW study of the self-esteem of high school girls. Explain why the results of the study are likely to be misleading. What data might be appropriate for assessing the self-esteem of high school girls?

   4. Refer to the Food Research and Action Center study of hunger in America. Explain why the results of the study are likely to be misleading. What data would provide insight into the proportion of hungry American children?