Lecture Data ans statistics Applications in Business and Economics

1.5 Statistical Inference
Many situations require information about a large group of elements (individuals, companies,
voters, households, products, customers, and so on). But, because of time, cost, and
other considerations, data can be collected from only a small portion of the group. The larger
group of elements in a particular study is called the population, and the smaller group is
called the sample. Formally, we use the following definitions.
1.5 Statistical Inference 15
POPULATION
A population is the set of all elements of interest in a particular study.
SAMPLE
A sample is a subset of the population.
The process of conducting a survey to collect data for the entire population is called a
census. The process of conducting a survey to collect data for a sample is called a sample
survey. As one of its major contributions, statistics uses data from a sample to make estimates
and test hypotheses about the characteristics of a population through a process
referred to as statistical inference.
As an example of statistical inference, let us consider the study conducted by Norris
Electronics. Norris manufactures a high-intensity lightbulb used in a variety of electrical
products. In an attempt to increase the useful life of the lightbulb, the product design group
developed a new lightbulb filament. In this case, the population is defined as all lightbulbs
that could be produced with the new filament. To evaluate the advantages of the new filament,
200 bulbs with the new filament were manufactured and tested. Data collected from
this sample showed the number of hours each lightbulb operated before filament burnout.
See Table 1.5.
Suppose Norris wants to use the sample data to make an inference about the average
hours of useful life for the population of all lightbulbs that could be produced with the
new filament. Adding the 200 values in Table 1.5 and dividing the total by 200 provides
the sample average lifetime for the lightbulbs: 76 hours. We can use this sample result
to estimate that the average lifetime for the lightbulbs in the population is 76 hours.
Figure 1.7 provides a graphical summary of the statistical inference process for Norris
Electronics.
Whenever statisticians use a sample to estimate a population characteristic of interest,
they usually provide a statement of the quality, or precision, associated with the estimate.