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### Chapter 1

An Introduction to Business Statistics

- When it is singular, it refers to the sciences of statistics that help us collect, organize, and interpret Data.
- When it is plural, it refers to the data themselves, especially those that describe or summarize something.

Measurement

The process of determining the extent, quantity, amount, etc, of the variable of interest for a particular item of the population.

- Produces data
- For example, collecting annual starting salaries of graduates from last year’s MBA program

Quantitative

The possible measurements are numbers that represent quantities, ‘how many ’ or ‘how much’

- A person’s weight is quantitative.
- A laptop’s price is also quantitative.

When initiating a study, we first define our variable of interest, or response variable. Other variables, called factors, may be related to the response variable interest will also be measured.

- When analysts are unable to control the factors of interest, the study is called observational.
- If we are able to set or manipulate the values of these factors, we have an experimental study.

Qualitative

A descriptive category to which a population unit belongs: a descriptive attribute of a population unit.

- A person’s gender is qualitative
- A person’s hair color is also qualitative

Census

The process of collecting the population of all measurements is a census.

- Census usually too expensive, too time consuming, and too much effort for a large population

Sample

A subset of population units.

- For example, a university graduated 8,742 students
- This is too large for a census
- So, we select a sample of these graduates and learn their annual starting salaries

Parameter vs. Statistic

- A parameter is a numerical description of a population characteristic.

Example: the percentage of college students who use Dell computer.

- A statistic is a numerical description of a sample characteristic.

Example: the percentage of students selected nationwide using Dell computer.

Descriptive Statistics

The science of describing the important aspects of a set of measurements.

- For example, for a set of annual starting salaries, want to know:
- How much to expect
- What is a high versus low salary
- If the population is small, could take a census and make statistical inferences
- But if the population is too large, then …

Statistical Inference

The science of using a sample of measurements to make generalizations about the important aspects of a population of measurements.

- For example, use a sample of starting salaries to estimate the important aspects of the population of starting salaries

Selecting a Random Sample

A random sample is a sample selected from a population so that:

- Every element in the population has the same chance of being included in the sample.
- Each possible sample (of the same size) has the same chance of being selected

Random Sample Example

- Randomly pick two different people from a group of 15:
- Number the people from 1 to 15 and write their numbers on 15 different slips of paper
- Thoroughly mix the papers and randomly pick two of them
- The numbers on the slips identifies the people for the sample

Drawing the Random Sample

- If the population is large, use a table of random numbers
- In large sampling projects, tables of random numbers are often used to automate the sample selection process
- See next slide a table of random numbers

Using Random Number Tables

- For a demonstration of the use of random numbers, read Example 1.1, “Cell Phone Case: Estimating Cell Phone Costs,” in the textbook
- Use random numbers to randomly select 100 employees from a bank with 2,136 employees
- Random numbers canbe computer-generated

Approximately Random Samples

- In general, must make a list identifying each and every individual population unit
- Called a frame
- If the population is very large, it may not be possible to list every individual population unit
- So instead draw a “systematic” sample

Systematic Sample

- Randomly enter the population and systematically sample every kth unit
- This usually approximates a random sample
- Read Example 1.2, “Marketing Research Case: Rating a New Bottle Design,” in the textbook

Systematic Sampling

- Select some starting point and then select every k th element in the population

Example 1.2: Rating a New Bottle Design

- Wish to determine consumer reaction to a new bottle design
- Will use the “mall intercept method”
- Shoppers in a mall are intercepted and asked to participate in a consumer survey
- Asked to rate anew bottle

Example 1.2: Using Systematic Sample

- Cannot list and number every shopper
- As a result, cannot use random numbers
- Instead, will use a systematic sample
- Every 100th shopper is selected
- Using every 100th shopper is arbitrary
- Using widely spaced shoppers, can be reasonable sure not related

Problems With Non-Random Samples

- For presidential election of 1936, Literary Digest predicted Alf Landon would defeat Franklin D. Roosevelt
- Instead Roosevelt won in a landslide
- Literary Digest’s mistake was to sample names from telephone books and club membership rosters
- Many people did not have phones or belong to clubs
- As a result, they were not included in sample
- They voted overwhelmingly for Roosevelt

Voluntary Response Sample

- Participants select themselves to be in the sample
- Participants “self-select”
- For example, voting on American Idol
- Commonly referred to as a “non-scientific” sample
- Usually not representative of the population
- Over-represent individuals with strong opinions
- Usually, but not always, negative opinions

Terminology

- Measurement
- Quantitative
- Qualitative
- Population of Measurement
- Census
- Sample
- Random Sample
- Descriptive Statistics
- Statistical Inference

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