SPEAKER WOOFER DRIVER MANUFACTURING
W. EDWARDS DEMING: TRANSFORMING INDUSTRY WITH SQC
William Edwards Demingwas born on October 14, 1900, in Sioux City, Iowa. Shortly after his birth, his father secured home- stead land and moved the family first to Cody, Wyoming, and then to Powell, Wyoming.
Deming obtained a B.S. in physics at the University of Wyoming in 1921, a master’s degree in physics and mathematics at the University of Colorado in 1924, and a doctorate in mathe- matical physics at Yale University in 1928.
While working for various federal agencies during the next decade, Deming became an expert on sampling and quality con- trol. In 1939, he accepted the position of head mathematician and advisor in sampling at the U.S. Census Bureau. Deming began the use of sampling at the Census Bureau and, expanding the work of Walter A. Shewhart (later known as the father of statistical qual- ity control, or SQC), also applied statistical methods of quality control to provide reliability and quality to the nonmanufacturing environment.
In 1946, Deming left the Census Bureau, joined the Graduate School of Business Administration at New York University, and offered his services to the private sector as a consultant in
statistical studies. It was in this last-named capacity that Deming transformed industry in Japan. Deming began his long association with Japanese businesses in 1947 when the U.S. War Department engaged him to instruct Japanese industrialists in statistical quality control methods. The reputation of Japan’s goods changed from definitely shoddy to amazingly excellent over the next two decades as the businessmen of Japan implemented Deming’s teachings.
More than 30 years passed before Deming’s methods gained widespread recognition by the business community in the United States. Finally, in 1980, as the result of the NBC white paper If Japan Can, Why Can’t We?, in which Deming’s role was publicized, executives of major corporations (among them, Ford Motor Company) contracted with Deming to improve the quality of U.S. goods.
Deming maintained an intense work schedule throughout his 80s, giving 4-day managerial seminars, teaching classes at NYU, sponsoring clinics for statisticians, and consulting with businesses internationally. His last book,The New Economics,was published in 1993. Dr. Deming died at his home in Washington, D.C., on December 20, 1993.
C H A P T E R
12 Inferences for Population Proportions
CHAPTER OUTLINE 12.1 Confidence Intervals
for One Population Proportion
12.2 Hypothesis Tests for One Population Proportion
12.3 Inferences for Two Population Proportions
CHAPTER OBJECTIVES
In Chapters 8–10, we discussed methods for finding confidence intervals and performing hypothesis tests for one or two population means. Now we describe how to conduct those inferences for one or two population proportions.
A population proportion is the proportion (percentage) of a population that has a specified attribute. For example, if the population under consideration consists of all Americans and the specified attribute is “retired,” the population proportion is the proportion of all Americans who are retired.
In Section 12.1, we begin by introducing notation and terminology needed to perform proportion inferences; then we discuss confidence intervals for one population proportion. Next, in Section 12.2, we examine a method for conducting a hypothesis test for one population proportion.
In Section 12.3, we investigate how to perform a hypothesis test to compare two population proportions and how to construct a confidence interval for the difference between two population proportions.
CASE STUDY
Arrested Youths
In aNew York Timesarticle titled
“Many in U.S. Are Arrested by Age 23, Study Finds,” E. Goode noted that, by age 23, almost a third of Americans have been arrested (excluding arrests for minor traffic
violations). The article reports on a recent study by R. Brame et al.
published as “Cumulative Prevalence of Arrest from Ages 8 to 23 in a National Sample” (Pediatrics, Vol. 129, No. 1, pp. 21–27). That study analyzed self-reported, arrest-history data from theNational Longitudinal Survey of Youth.
The results of the study suggest a substantial increase in the prevalence of youth (children and young adults) arrests since the last national study, which occurred in the 1960s. Furthermore, according to S. Bushway, a criminologist at the University of Albany and a co-author of the aforementioned paper, “This estimate provides a real sense that the proportion of people who have criminal history records is sizable and
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12.1 Confidence Intervals for One Population Proportion 567
perhaps much larger than most people would expect.”
Professor Brame, lead author of the paper and a criminologist at the University of North Carolina at Charlotte, told the reporter that he hoped the research would be useful to physicians in helping their young patients recover from being arrested.
More generally, the researchers concluded that “At a minimum, being arrested for criminal activity signifies increased risk of unhealthy
lifestyle, violence involvement, and violent victimization. Incorporating this insight into regular clinical assessment could yield significant benefits for patients and the larger community.”
After studying the inferential methods discussed in this chapter, you will be asked to conduct statistical analyses on arrests of American youths based on data presented in the researchers’
paper.
12.1 Confidence Intervals for One Population Proportion
Statisticians often need to determine the proportion (percentage) of a population that has a specified attribute. Some examples are
r the percentage of U.S. adults who have health insurance r the percentage of cars in the United States that are imports
r the percentage of U.S. adults who favor stricter clean air health standards r the percentage of Canadian women in the labor force.
In the first case, the population consists of all U.S. adults and the specified attribute is “has health insurance.” For the second case, the population consists of all cars in the United States and the specified attribute is “is an import.” The population in the third case is all U.S. adults and the specified attribute is “favors stricter clean air health standards.” In the fourth case, the population consists of all Canadian women and the specified attribute is “is in the labor force.”
We know that it is often impractical or impossible to take a census of a large pop- ulation. In practice, therefore, we use data from a sample to make inferences about the population proportion. We introduce proportion notation and terminology in the next example.
EXAMPLE 12.1 Proportion Notation and Terminology
Playing Hooky From Work Many employers are concerned about the problem of employees who call in sick when they are not ill. TheHilton Hotels Corporation commissioned a survey to investigate this issue. One question asked the respondents whether they call in sick at least once a year when they simply need time to relax.
For brevity, we use the phraseplay hookyto refer to that practice.
The survey polled 1010 randomly selected U.S. employees. The proportion of the 1010 employees sampled who play hooky was used to estimate the proportion of all U.S. employees who play hooky. Discuss the statistical notation and terminology used in this and similar studies on proportions.
Solution We usepto denote the proportion of all U.S. employees who play hooky;
it represents thepopulation proportionand is the parameter whose value is to be estimated. The proportion of the 1010 U.S. employees sampled who play hooky is designated pˆ (read “p hat”) and represents asample proportion;it is the statistic used to estimate the unknown population proportion, p.
Although unknown, the population proportion, p, is a fixed number. In contrast, the sample proportion, ˆp, is a variable; its value varies from sample to sample. For instance, if 202 of the 1010 employees sampled play hooky, then
ˆ
p= 202
1010 =0.2,
that is, 20.0% of the employees sampled play hooky. If 184 of the 1010 employees sampled play hooky, however, then
ˆ
p= 184
1010 =0.182, that is, 18.2% of the employees sampled play hooky.
These two calculations also reveal how to compute a sample proportion: Divide the number of employees sampled who play hooky, denotedx, by the total number of employees sampled,n. In symbols, ˆp=x/n. We generalize these new concepts below.
Exercise 12.9(a)–(b) on page 575