Chapter 1: The Nature of Statistics

Keno. In the game of keno, 20 balls are selected at random from 80 balls numbered 1-80. In Exercise 1.48 on page 16, you used simple random sampling to simulate one game of keno.

(a) Use systematic random sampling to obtain a sample of 20 of the 80 balls.

(b) Which method is easier: simple random sampling or systematic random sampling?

(c) Does it seem reasonable to use systematic random sampling to simulate one game of keno? Explain your answer.

Sampling Dorm Residents. Students in the dormitories of a university in the state of New York live in clusters of four double rooms, called suites. There are 48 suites, with eight students per suite.

(a) Describe a cluster sampling procedure for obtaining a sample of 24 dormitory residents.

(b) Students typically choose friends from their classes as suitemates. With that in mind, do you think cluster sampling is a good procedure for obtaining a representative sample of dormitory residents? Explain your answer.

(c) The university housing office has separate lists of dormitory residents by class level. The number of dormitory residents in each class level is as follows. Use the table to design a procedure for obtaining a stratified sample ( with proportional allocation ) of 24 dormitory residents.

Best High Schools. In an issue of Newsweek(Vol. CXLV, No. 20, pp. 48-57), B. Kantrowitz listed "The 100 best high schools in America" according to a ranking devised by J. Mathews. Another characteristic measured from the high school is the percent free lunch, which is the percentage of student body that is eligible for free and reduced-price lunches, an indicator of socioeconomic status. A percentage of 40% or more generally signifies a high concentration of children in poverty. The top 100 schools, grouped according to their percent free lunch, is as follows.

(a) Use the table to design a procedure for obtaining a stratified sample (with proportional allocation) of 25 high schools from the list of the top 100 ranked high schools.

(b) If stratified random sampling with proportional allocation is used to select the sample of 25 high schools, how many would be selected from the stratum with a percent-free-lunch value of 30-under 40?

U.S. House of Representatives. There are 435 representatives in the 113th session of the U.S. House of Representatives. On the website www.house.gov, you can find an alphabetized list of the 435 congresspersons. In 2013, the first representative listed is Robert Aderholt, a Republican from Alabama, and the last representative listed is Todd Young, a Republican from Indiana. Suppose that the alphabetized list is indexed 1 through 435.

(a) Use systematic random sampling to obtain a sample of 15 of the 435 representatives.

(b) Suppose that, in Step 2 of Procedure 1.1, the random number chosen is 12 (i.e., k = 12). Determine the sample.

Peace Corps Volunteers. The Peace Corps is an independent U.S. government agency that provides trained volunteers for countries requesting assistance. According to Peacecorps.org, as of September 2012, volunteers currently serve in about 76 different host countries. The average age of a volunteer is about 28 years old. The following table reports the percentage of total volunteers serving by geographic region.

(a) Use the table to design a procedure for obtaining a stratified sample (with proportional allocation) of 50 Peace Corps volunteers.

(b) If stratified random sampling with proportional allocation is used to select the sample of 50 Peace Corps volunteers, how many would be selected from the Caribbean?

The Terri Schiavo Case. In the early part of 2005, the Terri Schiavo case received national attention as her husband sought to have life support removed, and her parents sought to maintain that life support. The courts allowed the life support to be removed, and her death ensued. A Harris Poll of 1010 U.S. adults was taken by telephone on April 21, 2005, to determine how common it is for life support systems to be removed. Those questioned in the sample were asked: (1) Has one of your parents, a close friend, or a family member died in the last 10 years? (2) Before (this death/these deaths) happened, was this person/were any of these people, kept alive by any support system? (3) Did this person die while on a life support system, or had it been withdrawn? Respondents were also asked questions about age, sex, race, education, region, and household income to ensure that results represented a cross-section of U.S. adults.

(a) What kind of sampling design was used in this survey? Explain your answer

(b) If 78% of the respondents answered the first question in the affirmative, what was the approximate sample size for the second question?

(c) If 28% of those responding to the second question answered "yes," what was the approximate sample size for the third question?

In simple random sampling, all samples of a given size are equally likely. Is that true in systematic random sampling? Explain your answer.

In simple random sampling, it is also true that each member of the population is equally likely to be selected, the chance for each member being equal to the sample size divided by the population size.

(a) Under what circumstances is that fact also true for systematic random sampling? Explain your answer.

(b) Provide an example in which that fact is not true for systematic random sampling.

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.

Quick Vote. TalkBack Live, a production of CNN, conducted on-line surveys on various issues. One survey, called a QuickVote, of 680 people asked "Would you vote for a third-party candidate?" Of the 680 people surveyed, 608 ( 89.4 % ) responded "yes" and 72 ( 10.6 % ) responded "no." Beneath the vote tally, the following statement regarding the sampling procedure was found:

This QuickVote is not scientific and reflects the opinions of only those Internet users who have chosen to participate. The results cannot be assumed to represent the opinions of Internet users in general, nor the public as a whole. The Quick Vote sponsor is not responsible for content, functionality or the opinions expressed therein.

Discuss the preceding statement in light of what you have learned in this chapter.