The Nature of Statistics

Oklahoma State Officials. Refer to Table 5.1 on page 196. 

(a). List the possible samples without replacement of size 4 that can be obtained from the population of five officials. (Hint: There are five possible samples.) 

If a simple random sample without replacement of four officials is taken from the five officials, determine the probability that 

(b). the governor, secretary of state, attorney general, and treasurer are obtained. 

(c). the governor and treasurer are included in the sample. 

(d). the governor is included in the sample. 

Define the following terms:

(a) Population

(b) Sample

What are the two major types of statistics? Describe them in detail.

Identify some methods used in descriptive statistics.

Explain two ways in which descriptive statistics and inferential statistics are interrelated.

Define the following terms:

(a) Observational study

(b) Designed experiment 

Fill in the following blank:

Observational studies can reveal only association, whereas experiments can help establish              .

In Exercises 1.7-1.12, classify each of the studies as either descriptive or inferential. Explain your answers.

TV Viewing Times. Data from a sample of Americans yielded the following estimates of average TV viewing time per month for all Americans 2 years old and older. The times are in hours and minutes; Q1 stands for first quarter. [SOURCE: The Cross-Platform Report, Quarter 1, 2011. Published by The Nielsen Company, © 2011.]

In Exercises 1.7-1.12, classify each of the studies as either descriptive or inferential. Explain your answers.

Professional Athlete Salaries. From the Statistical Abstract of the United States and the article "Average Salaries in the NBA, NFL, MLB and NHL" by J. Dorish, published on the Yahoo! Contributor Network, we obtained the following data on average professional athletes' salaries for the years 2005 and 2011.

In Exercises 1.7-1.12, classify each of the studies as either descriptive or inferential. Explain your answers.

Home Sales.  Zillow.com is an online database that provides real estate information for U.S. homes that are for rent or sale. It also presents statistics on recently sold homes. The following table gives various information on all homes sold in several different cities across the United States for the month of September 2012.

In Exercises 1.7-1.12, classify each of the studies as either descriptive or inferential. Explain your answers.

Drug Use. The U.S. Substance Abuse and Mental Health Services Administration collects and publishes data on nonmedical drug use, by type of drug and age group, in National Survey on Drug Use and Health. The following table provides data for the years 2003 and 2008. The percentages shown are estimates for the entire nation based on information obtained from a sample (NA, not available).

In Exercises 1.7-1.12, classify each of the studies as either descriptive or inferential. Explain your answers.

Dow Jones Industrial Averages. From the Stock Performance Guide, published online by Istockl on the website 1Stock1.com, we found the closing values of the Dow Jones Industrial Averages as of the end of December for the years 2004 through 2013.

In Exercises 1.7-1.12, classify each of the studies as either descriptive or inferential. Explain your answers.

In-Demand College Majors. In a June 2013 article, published online by The Street, B. O'Connell discussed the results of a survey on opportunities for graduating college students. In one aspect of the survey, the following percentage estimates were reported on which college majors were in demand among U.S. firms. [SOURCE: "The Most In-Demand College Majors This Year." Published by Career-Builder, LLC, 2013.]

Thoughts on Evolution. In an article titled "Who has designs on your student's minds?" (Nature, Vol. 434, pp. 1062-1065), author G. Brumfiel postulated that support for Darwinism increases with level of education. The following table provides percentages of U.S. adults, by educational level, who believe that evolution is a scientific theory well supported by evidence.

(a) Do you think that this study is descriptive or inferential? Explain your answer.

(b) If, in fact, the study is inferential, identify the sample and population.

 Big-Banks Break-up. A nationwide survey of 1000 U.S. adults, conducted in March 2013 by Rasmussen Reports (field work by Pulse Opinion Research, LLC), found that 50% of respondents favored a plan to break up the 12 megabanks, which then controlled about 69% of the banking industry. 

(a) Identify the population and sample for this study. 

(b) Is the percentage provided a descriptive statistic or an inferential statistic? Explain your answer. 

Genocide. The document "American Attitudes about Genocide" provided highlights of a nationwide poll with 1000 participants. The survey, conducted by Penn Schoen Berland between June 30 and July 10, 2012, revealed that "66% of respondents believe that genocide is preventable." 

(a). Is the statement in quotes an inferential or a descriptive statement? Explain your answer. 

(b). Based on the same information, what if the statement had been "66% of Americans believe that genocide is preventable"?

Vasectomies and Prostate Cancer. Refer to the vasectomy/ prostate cancer study discussed in Example 1.5 on page 6. 

(a). How could the study be modified to make it a designed experiment? 

(b). Comment on the feasibility of the designed experiment that you described in part (a).

In Exercises 1.17-1.22, state whether the investigation in question is an observational study or a designed experiment. Justify your answer each case.

The Salk Vaccine. In the 1940s and early 1950s, the public greatly concerned about polio. In an attempt to prevent this disease, Jonas Salk of the University of Pittsburgh developed a polio vaccine. In a test of the vaccine's efficacy, involving nearly million grade-school children, half of the children received the Salk vaccine; the other half received a placebo, in this case, an injection of salt dissolved in water. Neither the children nor the doctors performing the diagnoses knew which children belonged to which group, but an evaluation center did. The center found that the incidence of polio was far less among the children inoculated with the Salk vaccine. From that information, the researchers concluded that the vaccine would be effective in preventing polio for all U.S. school children; consequently, it was made available for general use.

In Exercises 1.17-1.22, state whether the investigation in question is an observational study or a designed experiment. Justify your answer in each case.

Do Left-Handers Die Earlier? According to a study published in the Journal of the American Public Health Association, left-handed people do not die at an earlier age than right-handed people, contrary to the conclusion of a highly publicized report done 2 years earlier. The investigation involved a 6-year study of 3800 people in East Boston older than age 65. Researchers at Harvard University and the National Institute of Aging found that the "lefties" and "righties" died at exactly the same rate. "There was no difference, period," said Dr. J. Guralnik, an epidemiologist at the institute and one of the coauthors of the report.

In Exercises 1.17-1.22, state whether the investigation in question is an observational study or a designed experiment. Justify your answer in each case.

Sex, Sleep, and PTSD. In the article, "One's Sex, Sleep, and Posttraumatic Stress Disorder" (Biology of Sex Differences, Vol. 3, No. 29, pp. 1-7), I. Kobayashi et al. study the relationship between one's sex, sleep patterns, and posttraumatic stress disorder (PTSD) after trauma exposure. The authors report that women have a higher lifetime prevalence of PTSD as well as a greater risk of developing PTSD following trauma exposure. Relationships between sleep and physical health have been documented in a number of studies, and the authors explore the possibility that disruptive sleep habits are common among people with PTSD and also a possible risk factor for the development of PTSD. A questionnaire of men and women with and without PTSD produced data on their sleep habits.

In Exercises 1.17-1.22, state whether the investigation in question is an observational study or a designed experiment. Justify your answer in each case.

Aspirin and Cardiovascular Disease. In the article by P. Ridker et al. titled "A Randomized of Low-dose Aspirin in the Primary Prevention of Cardiovascular Disease in Women" (New England Journal of Medicine, Vol. 352, pp. 1293–1304), the researchers noted that "We randomly assigned 39,876 initially healthy women 45 years of age or older to receive 100 mg of aspirin or placebo on alternate days and then monitored them for 10 years for a first major cardiovascular event (i.e., nonfatal myocardial infarction, non-fatal stroke, death from cardiovascular causes)."

In Exercises 1.17-1.22, state whether the investigation in question is an observational study or a designed experiment. Justify your answer in each case.

Starting Salaries. The National Association of Colleges and Employers (NACE) compiles information on salary offers to new college graduates and publishes the results in Salary Survey. 

Do you think that these rates are descriptive statistics or inferential statistics? Explain your answer.

In Exercises 1.17-1.22, state whether the investigation in question is an observational study or a designed experiment. Justify your answer in each case.

Heart Failure. In the paper "Cardiac-Resynchronization Therapy with or without an Implantable Defibrillator in Advanced Chronic Heart Failure" (New England Journal of Medicine, Vol. 350, pp. 2140-2150), M. Bristow et al. reported the results of a study of methods for treating patients who had advanced heart failure due to ischemic or nonischemic cardiomyopathies. A total of 1520 patients were randomly assigned in a 1:2:2 ratio to receive optimal pharmacologic therapy alone or in combination with either a pacemaker or a pacemaker-defibrillator combination. The patients were then observed until they died or were hospitalized for any cause.

Lobbying Congress.  In the special report, "Bitter Pill: Why Medical Bills Are Killing Us" (TIME, Vol. 181, No. 8, 2013), S. Brill presented an in-depth investigation of hospital billing practices that reveals why U.S. health care spending is out of control. One of the many statistics provided in the report is that, during the period from 1998 through 2012, the pharmaceutical and health-care-products industries and organizations representing doctors, hospitals, nursing homes, health services, and HMOs spent \(5.36 billion lobbying Congress. 

(a). Under what conditions would the \)5.36 billion lobbying-expenditure figure be a descriptive statistic? Explain your answer. 

(b). Under what conditions would the $5.36 billion lobbying- expenditure figure be an inferential statistic? Explain your answer.

Medical Testing on Animals. In its Summer 2013 Animal Action Report, the National Anti-Vivisection Society stated that "59% of Americans between the ages of 18 and 29 oppose medical testing on animals." The percentage of 59% was computed from sample data. 

(a). Identify the population under consideration. 

(b). Identify the sample under consideration. 

(c). Is the statement in quotes descriptive or inferential? 

(d). If you wanted to make it clear that the percentage of 59% was computed from sample data, how would you rephrase the statement in quotes?

Ballistic Fingerprinting. In an on-line press release, ABCNews.com reported that "...73 percent of Americans... favor a law that would require every gun sold in the United States to be test-fired first, so law enforcement would have its fingerprint in case it were ever used in a crime." 

(a). Do you think that the statement in the press release is inferential or descriptive? Can you be sure? 

(b). Actually, ABCNews.com conducted a telephone survey of a random national sample of 1032 adults and determined that 73% of them favored a law that would require every gun sold in the United States to be test-fired first, so law enforcement would have its fingerprint in case it were ever used in a crime. How would you rephrase the statement in the press release to make clear that it is a descriptive statement? an inferential statement? 

Causes of Death. The National Center for Health Statistics published the following data on the leading causes of death in 2010 in National Vital Statistics Reports. Deaths are classified according to the tenth revision of the International Classification of Diseases. 

Rates are per 100,000 population.

Explain why a census is often not the best way to obtain information about a population.

Identify two statistical methods other than a census for obtaining information.

In sampling, explain why obtaining a representative sample is important.

Provide a scenario of your own in which a sample is not representative.

Regarding probability sampling:

(a) What is it?

(b) Does probability sampling always yield a representative sample?

(c) Identify some advantages of probability sampling.

Regarding simple random sampling:

(a) What is simple random sampling?

(b)  What is a simple random sample?

(c) Identify two forms of simple random sampling and explain the difference between the two.

The inferential procedures discussed in this book are intended for use with only one particular sampling procedure. What sampling procedure is that?

Identify two methods for obtaining a simple random sample.

What is the acronym used for simple random sampling without replacement?

The members of a population are numbered 1-5.

(a) List the 10 possible samples (without replacement) of size 3 from this population.

(b) SRS of size 3 is taken from the population, what are the chances of selecting 1, 3, and 5? Explain your answer.

(c) Use Table I in Appendix A to obtain an SRS of size 3 from the population. Start at the single-digit number in line number 5 and column number 20, read down the column, up the next, and so on.

The members of a population are numbered 1-4.

(a). List the 6 possible samples (without replacement) of size 2 from this population. 

(b). If an SRS of size 2 is taken from the population, what are the chances of selecting 2 and 3? Explain your answer.

(c). Use Table I in Appendix A to obtain an SRS of size 2 from the population. Start at the single-digit number in line number 17 and column number 7, read down the column, up the next, and so on.

The members of a population are numbered 1-90.

(a). Use Table I in Appendix A to obtain SRS of size 5 from the population. Start at the two-digit number in line number 15 and column numbers 25-26, read down the column, up the next, and so on.

(b). If you have access to a random-number generator, use it to solve part (a).

The members of a population are numbered 1-50.

(a). Use Table I in Appendix A to obtain an SRS of size 6 from the population. Start at the two-digit number in line number 10 and column numbers 10-11, read down the column, up the next, and so on.

(b). If you have access to a random-number generator, use it to solve part (a)

Memorial Day Poll. In the year 2000, an on-line poll was conducted over Memorial Day weekend that asked people what they were doing to observe the holiday. 

The choices were: (1) stay home and relax, (2) vacation outdoors over the weekend, or (3) visit a military cemetery. 

More than 22,000 people participated in the poll, with 86% selecting option 1. Discuss this poll with regard to its suitability.

Best-Selling Albums. Refer to Exercise 1.44. 

(a). List the 15 possible samples (without replacement) of four artists that can be selected from the six. 

(b). Describe a procedure for taking a simple random sample of four artists from the six. 

(c). If a simple random sampling procedure is used to obtain four artists, what are the chances of selecting E, A, L, and B? P, B, M, and A?

Best-Selling Albums. The Recording Industry Association of America provides data on the best-selling albums of all time. As of May 28, 2013, the top six best-selling albums of all time (U.S. sales only), are by the artists the Eagles (E), Michael Jackson (M), Pink Floyd (P), Led Zeppelin (L), AC/DC (A), and Billy Joel (B). 

(a). List the 15 possible samples (without replacement) of two artists that can be selected from the six. For brevity, use the initial provided. 

(b). Describe a procedure for taking a simple random sample of two artists from the six. 

(c). If a simple random sampling procedure is used to obtain two artists, what are the chances of selecting P and A? M and E?

Oklahoma State Officials. The five top Oklahoma state officials are displayed in Table 1.2 on page 11. Use that table to solve the following problems.

(a). List the 10 possible samples (without replacement) of size 3 that can be obtained from the population of five officials.

(b). If a simple random sampling procedure is used to obtain a sample of three officials, what are the chances that it is the first sample on your list in part (a)? the second sample? the tenth sample? 

Oklahoma State Officials. The five top Oklahoma state officials are displayed in Table 1.2 on page 11. Use that table to solve the following problems. 

(a) List the possible samples of size 1 that can be obtained from the population of five officials.

(b) What is the difference between obtaining a simple random sample of size 1 and selecting one official at random? 

(c) List the possible samples (without replacement) of size 5 that can be obtained from the population of five officials. 

(d) What is the difference between obtaining a simple random sample of size 5 and taking a census of the five officials?

Estimating Median Income.  Explain why a sample of 30 dentists from Seattle taken to estimate the median income of all Seattle residents is not representative.

Social Networking Websites. From Wikipedia.com, we obtained the top seven major active social networking websites in the United States, excluding dating websites. Ranked according to registered users, as of April 2013, from most popular to least popular, they are Facebook (F), Twitter (T), Goggle+ (G), Habbo (H), LinkedIn (L), Bebo (B), and Tagged (A). 

(a) List the 21 possible samples (without replacement) of two social media websites that can be selected from the seven. For brevity, use the initial provided. 

(b) If a simple random sampling procedure is used to obtain two of these social media websites, what are the chances of selecting B and A? T and G?

Best-Selling Albums. Refer to Exercise 1.44. 

(a) List the 20 possible samples (without replacement) of three artists that can be selected from the six. 

(b) Describe a procedure for taking a simple random sample of three artists from the six.

(c) If a simple random sampling procedure is used to obtain three artists, what are the chances of selecting M, A, and L? P, L, and E?

Keno. In the game of keno, 20 balls are selected at random from 80 balls numbered 1-80. 

(a) Use Table I in Appendix A to simulate one game of keno by obtaining 20 random numbers between 1 and 80. Start at the two-digit number in line number 5 and column numbers 31-32, read down the column, up the next, and so on.

(b) If you have access to a random-number generator, use it to solve part (a).

The International 500. Each year, Fortune Magazine publishes an article titled "The International 500" that provides a ranking by sales of the top 500 firms outside the United States. Suppose that you want to examine various characteristics of successful firms. Further suppose that, for your study, you decide to take a simple random sample of 10 firms from Fortune Magazine's list of "The International 500."

(a) Use Table I in Appendix A to obtain 10 random numbers that you can use to specify your sample. Start at the three-digit number in line number 14 and column numbers 10-12, read down the column, up the next, and so on. 

(b) If you have access to a random-number generator, use it to solve part (a).