Chapter 1 - Introduction to Statistics PDF

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CHAPTER 1 Introduction to the Practice of Statistics Objectives 1. Define statistics and statistical thinking 2. Explain the process of statistics 3. Distinguish between quantitative (metric) and qualitative (non-metric) variables 4. Distinguish between discrete and continuous variables Statistics is the science of collecting, organizing, summarizing, and analyzing data to draw conclusions or answer questions.

Population: The entire group to be studied. Sample: Subset of the population that is being studied. Individual: Person or object that is a member of the population being studied. Parameter: A numerical summary of a population Statistic: A numerical summary of a sample. Descriptive statistics: Consist of organizing and summarizing data. Descriptive statistics describes data through numerical summaries, tables, and graph. The main purpose is to provide an overview of the information collected. Inferential statistics: Uses methods that take a result from a sample, extend it to the population, and measure the reliability of the result.

Parameters are generally unknown because it is difficult to gather all information about the population due to time, money, and other factors. What we do instead is gather sample of size n from a population of size N and obtain a statistic from the sample. That statistic will be used to estimate the population parameter.

Example 1. A quality control manager randomly selects 50 bottles of CocaCola that were filled on October 15 in order to assess the calibration of the filling machine. Identify the population and the sample.

Example 2. Which of the follow is a parameter or statistic (a) Suppose the percentage of all students on your campus who own a car is 48.2%.

(b) Suppose a sample of 100 students is obtained, and from this sample we find that 46% own a car.

Because data can vary, the results (answers) that we obtain using data can vary as well. This is a very different idea than what we are used to from previous mathematics courses. For example, if Bob and Barb were asked to solve the equation 3x+5=11, they would both get x=2, if they use correct procedures. In statistics, if Bob and Barb are asked to estimate the average commute time for Cypress College students, they would most likely get different answers since they would ask different people and get different data, even though both of their procedures are correct. The only way they would get the exact answer is if they asked all of the same people. Variables: Characteristics of the individuals within the population. Variables can be classified into two groups: quantitative (metric) or qualitative (non-metric). Note: Sometimes qualitative variables are referred to as categorical variables. 1. ____________________________________ provides numerical measures of individuals. 2. ____________________________________ allows for classification of individuals based on some attribute or characteristic. Example 3. A researcher studied factors that affect the eating habits of adults in their mid-thirties. Classify each of the following variables considered in the study as qualitative or quantitative. a. Nationality b.

Number of children

c.

Household income in the previous year

d.

Level of education

e.

Daily intake of whole grains (measured in grams per day)

Quantitative variables can be further classified into two types: ________________________ variables that have either a finite number of possible values or a countable number of possible values (0, 1, 2, 3, …). ________________________ variable that has an infinite number of possible values that are not countable. Usually obtained by measuring.

Example 4. Determine whether the quantitative variables are discrete or continuous. (a) The number of heads obtained after flipping a coin five times. (b) The number of cars that arrive at a McDonald’s drive-thru between 12:00 P.M. and 1:00 P.M. (c) The distance a 2011 Toyota Prius can travel in city driving condition with a full tank of gas. (d) Time spent studying for an exam.

Levels of Measurement 1. A variable is at the ___________________ level of measurement if the values of the variable name, label, or categorize individuals. In addition, the naming scheme does not allow for the values of the variable to be arranged in a ranked or specific order. • Example: Eye color is at the nominal level because it only allows for categorization of brown, blue, green, etc. Also, it is not possible to rank eye color classifications. 2. A variable is at the __________________ level of measurement if it has the properties of the nominal level of measurement, however the naming scheme allows for the values of the variable to be arranged in a ranked or specific order. • Example: Letter grade is at the ordinal level because the values of the variable can be ranked, but differences in values have no meaning. For example, A is better than B, but A – B has no meaning. 3. A variable is at the __________________ level of measurement if it has the properties of the ordinal level of measurement and the differences in the values of the variable have meaning. A value of zero does not mean the absence of the quantity. Arithmetic operations such as addition and subtraction can be performed on values of the variable. • Example: Temperature is at the interval level because differences in the value of the variable make sense. For example, 70ᵒF - 60ᵒF = 10ᵒF has meaning. Also, 0ᵒF does not represent the absence of temperature. 4. A variable is at the _________________ level of measurement if it has the properties of the interval level of measurement and the ratios of the values of the variable have meaning. A value of zero means the absence of the quantity. Arithmetic operations such as multiplication and division can be performed on the values of the variable. • Example: Number of days during the past week that a college student studied is at the ratio level since the ratio of two values makes sense. For example, comparing a student who studied for 6 days studied twice as much as a student who studied for 3 days. Also, having a value of zero represents the absence of the variable. For example, a student who studied for zero days represents the absence of them studying. Example 5. Determine the level of measurement. (a) Movie ratings of zero to five stars _____________________________________ (b) Number of students at the bookstore at 2pm__________________________________ (c) The eye color of a group of kids at a pre-school _______________________________ (d) Letter grade in a class __________________________ (e) Time is takes to run a mile____________________________...