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QUAN 2010 Notes Introduction to Business Statistics

Lauren M. Nelsen and Kimberly Swetz

Section 1.1 Introduction to Statistics

Subsection 1.1.1 What is Statistics?

Question 1.1.1.

What is statistics?
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Answer.
the mathematical science that deals with the collection, analysis, and presentation of data, that is then used for inference and induction
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Question 1.1.2.

What is data?
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Answer.
the values assigned to observations or measurements
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Subsection 1.1.2 Branches of Statistics:

The three main branches of statistics are:
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  • Goal of descriptive statistics: to summarize data quickly to get an overview of the information
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  • predictive statistics analyzes past data to predict future values and aid in making well-informed decisions
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  • During our study of inferential statistics, we will learn a variety of techniques that allow us to draw conclusions about a population based on a sample of data.
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Question 1.1.3.

In our study of inferential statistics, we might want to ask a question such as the following:
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What is the average number of hours per week worked by students at UCCS?
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How would you answer this question?
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Subsection 1.1.3 Definitions and Terms

Definition 1.1.4.

  • population: set containing all the people or objects whose properties are to be described and analyzed by the data collector
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  • sample: a subset or subgroup of the population
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Definition 1.1.5.

  • parameter: number that describes a characteristic of a population
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  • statistic: a number that describes a characteristic of a sample
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Exercise 1.1.6.

A group of hotel owners in a large city decide to conduct a survey among citizens of the city to discover their opinions about casino gambling.
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(a)
Describe the population
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Answer.
The population is the set containing all citizens of the city.
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(b)
One of the hotel owners suggests obtaining a sample by surveying all the people at six of the largest nightclubs in the city on a Saturday night. The people surveyed will be asked to express their opinion on casino gambling. Does this seem like a good idea?
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Answer.
No, it does not! The people at the nightclub might not have the same attitude toward casino gambling as the population of all the city’s citizens.
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Exercise 1.1.7. Parameter vs. Statistic.

Definition 1.1.8.

A random sample is a sample obtained in such a way that every element in the population has an equal chance of being selected for the sample.
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Exercise 1.1.9.

Think again about the group of hotel owners from Exercise 1.1.6 who are in a large city and are interested in how the city’s citizen’s feel about casino gambling. Which of the following would be the most appropriate way to select a random sample?
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  • Randomly survey people who live in the oceanfront condominiums in the city.
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  • Survey the first 200 people whose names appear in the city’s telephone directory.
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  • Randomly select neighborhoods of the city and then randomly survey people within the selected neighborhoods.
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Definition 1.1.10.

Regardless of the sampling technique used, the sample should exhibit characteristics typical of those possessed by the target population.
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This type of sample is called a representative sample.
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