SPEAKER WOOFER DRIVER MANUFACTURING
W. EDWARDS DEMING: TRANSFORMING INDUSTRY WITH SQC
in Sioux City, Iowa. Shortly after his birth, his father se- cured homestead 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 math- ematics at the University of Colorado in 1924, and a doc- torate in mathematical physics at Yale University in 1928.
While working for various federal agencies during the next decade, Deming became an expert on sampling and quality control. In 1939, he accepted the position of head mathematician and advisor in sampling at the U.S. Cen- sus 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 quality control, or SQC), also applied statistical methods of qual- ity control to provide reliability and quality to the nonman- ufacturing 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. Dem- ing 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 Dem- ing’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 paperIf Japan Can, Why Can’t We?,in which Deming’s role was publicized, executives of major corpo- rations (among them, Ford Motor Company) contracted with Deming to improve the quality of U.S. goods.
Deming maintained an intense work schedule through- out his 80s, giving 4-day managerial seminars, teach- ing 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
Healthcare in the United States
One of the most important and controversial challenges facing the United States is healthcare. For many years now, the situation in U.S. healthcare has been deteriorating, measured by
insurability, affordability, percentage of gross domestic product (GDP), and performance.
For instance, according to the documentOECD Health Data, published by theOrganization for Economic Cooperation and
Development (OECD), in 2005, the per capita health expenditure in the United States was $6278, almost two and one-half times that of the average of $2549 of the other 29 countries surveyed. In addition, as a percentage of GDP, total healthcare expenditures in the United States were 15.3%, almost 75% more than the average of 8.75%
of the other 29 countries surveyed.
Moreover, the OECD reported that the United States ranks poorly among those countries on measures of life expectancy, infant mortality, and reductions in deaths from certain causes that should not occur in the presence of timely and effective healthcare.
Unlike the United States, most of the developed nations have some type of universal healthcare, in which everyone is covered. One particular 544
type of universal healthcare is single-payer healthcare, a national health plan financed by taxpayers in which all people get their insurance from a single government plan.
In July 2008, theCalifornia Nurses AssociationandNational Nurses Organizing Committeepublished the article “The Polling Is Quite Clear: The American Public Supports Guaranteed Healthcare on the
‘Medicare for All’ or ’Single-Payer’
Model.” This article contained data from four different national polls. We
reproduce the results of two of the polls from 2007. Furthermore, a March 2008 survey of 2000 American doctors, conducted by theIndiana University School of Medicine, found that 59% support a “Medicare for All”/single-payer healthcare system.
After studying the inferential methods discussed in this chapter, you will be able to conduct statistical analyses on the aforementioned polls to see for yourself the feelings of all Americans and their doctors on healthcare choices.
Do you support a single-payer healthcare system, that is, a national health plan financed by taxpayers in which all Americans would get their insurance from a single government plan?
Gallup Poll, n 1014 adults Associated Press/Yahoo News Poll, n 1821 adults, MoE 2.3
Is it the responsibility of the federal government to make sure all Americans have healthcare coverage?
Yes
64% 33%
No
3%
Unsure Yes
54% 44%
No
2%
Not answered
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 population. 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.
546 CHAPTER 12 Inferences for Population Proportions
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 use p to 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, p, is a variable; its value varies from sample to sample. Forˆ 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, pˆ =x/n. We generalize these new concepts below.
Exercise 12.5(a)–(b) on page 553