What is statistics?
Answer.
the mathematical science that deals with the collection, analysis, and presentation of data, that is then used for inference and induction
Section 1.1 Introduction to Statistics
Question 1.1.1.
Question 1.1.2.
What is data?
Answer.
the values assigned to observations or measurements
Subsection 1.1.1 Branches of Statistics:
The three main branches of statistics are:
- descriptive
- inferential
- predictive
- Goal of descriptive statistics: to summarize data quickly to get an overview of the information
- predictive statistics analyzes past data to predict future values and aid in making well-informed decisions
- 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.
Question 1.1.3.
In our study of inferential statistics, we might want to ask a question such as the following:
What is the average number of hours per week worked by students at UCCS?
How would you answer this question?
Subsection 1.1.2 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
- sample: a subset or subgroup of the population
Definition 1.1.5.
- parameter: number that describes a characteristic of a population
- statistic: a number that describes a characteristic of a sample
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.
(a)
Describe the population
Answer.
The population is the set containing all citizens of the city.
(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?
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.
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.
Exercise 1.1.9.
- Randomly survey people who live in the oceanfront condominiums in the city.
- Survey the first 200 people whose names appear in the city’s telephone directory.
- Randomly select neighborhoods of the city and then randomly survey people within the selected neighborhoods.
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?
Definition 1.1.10.
Regardless of the sampling technique used, the sample should exhibit characteristics typical of those possessed by the target population.
This type of sample is called a representative sample.
