Chapter 1: The Nature of Statistics

The members of a population have been numbered 1-500. A sample of size 10 is to be taken from the population, using stratified random sampling with proportional allocation. The strata are of sizes 200, 150, and 150, where stratum #1 consists of the members of the population numbered 1-200, stratum #2 consists of the members of the population numbered 201-350, and so forth.

(a) Determine the sample sizes that will be taken from the strata.

(b) Apply Procedure 1.3 on page 21 to determine the sample (i.e., the numbers corresponding to the members of the population that are included in the sample).

Ghost of Speciation Past. In the article, "Ghost of Speciation Past" (Nature, Vol. 435, pp. 29-31), T. Kocher looked at the origins of a diverse flock of cichlid fishes in the lakes of southeast Africa. Suppose that you wanted to select a sample from the hundreds of species of cichlid fishes that live in the lakes of southeast Africa. If you took a simple random sample from the species of each lake and combined all the simple random samples into one sample, which type of sampling design would you have used? Explain your answer.

Number of Farms.The National Agricultural Statistics Service (NASS) conducts studies of the number of acres devoted to farms in each county of the United States. Suppose that we divide the United States into the four census regions (Northeast, North Central, South, and West), take a simple random sample of counties from each of the four regions, and combine all four simple random samples into one sample. What type of sampling design have we used? Explain your answer.

John F. Kennedy. In one of his books, Ted Sorenson, Special Counsel to President John F. Kennedy, presents an intimate biography of the extraordinary man. According to Sorenson, Kennedy "read every fiftieth letter of the thirty thousand comings weekly to the White House." What type of sampling design was Kennedy using in this case? Explain your answer. [SOURCE: FromKennedy: The Classical Biography by Ted Sorenson. Published by Harper Perennial, © 2009.]

Litigation Surveys. In the article, "Non - probability Sampling Designs for Litigation Surveys (Trademark Reporter, Vol. 81, pp. 169-179), J. Jacoby and H. Handlin discussed the controversy about whether nonprobability samples are acceptable as evidence in litigation. The authors randomly selected 26 journals from a list of 1285 scholarly journals in the social and behavioral sciences. They examined all articles published during one year in each of the 26 journals selected with regard to sampling methods. What type of sampling design was used by these two authors in their investigation? Explain your answer.

Immunization of Schoolchildren. In the article, "Reasons for Non - uptake of Measles, Mumps, and Rubella Catch Up Immunisation in a Measles Epidemic and Side Effects of the Vaccine" (British Medical Journal,Vol. 310, pp. 1629-1632), R. Roberts et al . discussed a follow-up survey to examine why almost 10,000 children, ages 11-15, whose records showed no previous immunization were not immunized. In the survey, 10 of the 46 schools participating in the immunization campaign were randomly chosen and then the parents of all the nonimmunized children at the 10 selected schools were sent a questionnaire. What type of sampling design was used by these authors in their survey? Explain your answer.

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.]

Top North American Athletes. As part of ESPN's SportsCenturyRetrospective, a panel chosen by ESPN ranked the top 100 North American athletes of the twentieth century. For a class project, you are to obtain a simple random sample of 15 of these 100 athletes and briefly describe their athletic feats.

(a) Explain how you can use Table I in Appendix A to obtain the simple random sample.

(b) Starting at the three-digit number in line number 10 and column numbers 7-9 of Table I, read down the column, up the next, and so on, to find 15 numbers that you can use to identify the athletes to be considered.

(c) If you have access to a random-number generator, use it to obtain the required simple random sample

University Parking Facilities. During one year, a university wanted to gauge the sentiment of the people using the university's parking facilities. Each of the 8493 people that used the parking facilities had a sticker with a unique number between 1 and 8493. The university committee on parking decided to sample 30 users of the parking facilities and obtain their views on those facilities. The committee selected a number at random between 1 and 283 and got the number 10. The people interviewed were the ones whose stickers had numbers 10, 293, 576, ..., 8217. What type of sampling design was used by the university committee on parking? Explain your answer.

The International 500. In Exercise 1.49 on page 16, you used simple random sampling to obtain a sample of 10 firms from Fortune Magazine's list of "The International 500."

(a) Use systematic random sampling to accomplish that same task.

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

(c) Does it seem reasonable to use systematic random sampling to obtain a representative sample? Explain your answer.