A Note to the Student

1.5 Summary

The discipline of statistics and those who apply the tools of that discipline deal with Learning from Data. Medical researchers, social scientists, accountants, agron- omists, consumers, government leaders, and professional statisticians are all in- volved with data collection, data summarization, data analysis, and the effective communication of the results of data analysis.

1.6 Exercises

1.1 Introduction

Bio. 1.1 Selecting the proper diet for shrimp or other sea animals is an important aspect of sea farm- ing. A researcher wishes to estimate the mean weight of shrimp maintained on a specific diet for a period of 6 months. One hundred shrimp are randomly selected from an artificial pond and each is weighed. a. Identify the population of measurements that is of interest to the researcher. b. Identify the sample. c. What characteristics of the population are of interest to the researcher? d. If the sample measurements are used to make inferences about certain characteristics of the population, why is a measure of the reliability of the inferences important? Env. 1.2 Radioactive waste disposal as well as the production of radioactive material in some mining operations are creating a serious pollution problem in some areas of the United States. State health officials have decided to investigate the radioactivity levels in one suspect area. Two hun- dred points in the area are randomly selected and the level of radioactivity is measured at each point. Answer questions a, b, c, and d in Exercise 1.1 for this sampling situation. Soc. 1.3 A social researcher in a particular city wishes to obtain information on the number of chil- dren in households that receive welfare support. A random sample of 400 households is selected from the city welfare rolls. A check on welfare recipient data provides the number of children in each household. Answer questions a, b, c, and d in Exercise 1.1 for this sample survey. Gov. 1.4 Because of a recent increase in the number of neck injuries incurred by high school football players, the Department of Commerce designed a study to evaluate the strength of football helmets worn by high school players in the United States. A total of 540 helmets were collected from the five companies that currently produce helmets. The agency then sent the helmets to an independent testing agency to evaluate the impact cushioning of the helmet and the amount of shock transmitted to the neck when the face mask was twisted. a. What is the population of interest? b. What is the sample? c. What variables should be measured? d. What are some of the major limitations of this study in regard to the safety of helmets worn by high school players? For example, is the neck strength of the player related to the amount of shock transmitted to the neck and whether the player will be injured? Pol. Sci. 1.5 During the 2004 senatorial campaign in a large southwestern state, the issue of illegal im- migration was a major issue. One of the candidates argued that illegal immigrants made use of ed- ucational and social services without having to pay property taxes. The other candidate pointed out that the cost of new homes in their state was 20 –30 less than the national average due to the low wages received by the large number of illegal immigrants working on new home construction. A random sample of 5,000 registered voters were asked the question, “Are illegal immigrants generally a benefit or a liability to the state’s economy?” The results were 3,500 people responded “liability,” 1,500 people responded “benefit,” and 500 people responded “uncertain.” a. What is the population of interest? b. What is the population from which the sample was selected? c. Does the sample adequately represent the population? d. If a second random sample of 5,000 registered voters was selected, would the results be nearly the same as the results obtained from the initial sample of 5,000 voters? Explain your answer. Edu. 1.6 An American History professor at a major university is interested in knowing the history lit- eracy of college freshmen. In particular, he wanted to find what proportion of college freshman at the university knew which country controlled the original 13 states prior to the American Rev- olution. The professor sent a questionnaire to all freshmen students enrolled in HIST 101 and re- ceived responses from 318 students out of the 7,500 students who were sent the questionnaire. One of the questions was, “What country controlled the original 13 states prior to the American Revolution?” a. What is the population of interest to the professor? b. What is the sampled population? c. Is there a major difference in the two populations. Explain your answer. d. Suppose that several lectures on the American Revolution had been given in HIST 101 prior to the students receiving the questionnaire. What possible source of bias has the professor introduced into the study relative to the population of interest?