Introduction to Probability and Statistics

• The Role of Statistics

• Population and Sample

• Identify a Statistical Population

• Why Take a Sample of Data?

• The Reasons for Taking a Sample

• Categorical Data and Numerical Data: Discrete Vs Continuous

• Classifying Data

• Population Parameters Vs Sample Statistics

• Parameters and Statistics

• Descriptive Statistics Vs Inferential Statistics

• Simple Random Samples

• Section 1 Mixed Practice

• Organizing and Presenting Data

• Relative Frequency

• Histograms

• Left-End-Point Convention

• Simplifying an Expression in Summation Notation

• Simplify an Expression Using Summation Notation

• Four Important Properties of the Mean

• Identifying Situations Where the Mean, Median, and Mode Should be Used

• Identify Situations Where the Mean, Median, and Mode Should be Used

• Categorize a Distribution as Either Left Skewed, Right Skewed, or Symmetric

• The Role of Measures of Dispersion in Descriptive Statistics

• Identify the Role of Measures of Dispersion in Descriptive Statistics

• Determine when the Range is an Appropriate Measure of Dispersion

• Standard Deviation and Variance

• The Standard Deviation and Variance

• Calculate the Standard Deviation for a Set of Data

• Chebyshev’s Theorem

• Calculate the Minimum Percentage of Data Inside a Symmetric Interval

• Calculate the Maximum Percentage of Data Outside a Symmetric Interval

• Create an Interval that Captures At Least 1-1k^2 of the Data

• The Empirical Rule

• Form an Interval that Captures Approximately X% of the Data

• Use the Empirical Rule to determine the Percentage of Data Inside an Interval

• Contrast the Use of Chebyshev's Theorem and the Empirical Rule

• Calculate and Interpret Z-scores (as a Measure of Unusualness)

• Use Z Scores to Compare the Relative Standing of Two Measurements

• Mixed Practice Sections 1 and 2

• Basic Probability

• Basic Probability Approach

• Know When to Assume Equally Likely Outcomes When Calculating Probability

• Calculate Basic Probability

• Explain the Law of Large Numbers

• Discuss the Minimum and Maximum Likelihood of an Event

• Interpret a Given Probability Value

• Use the Fundamental Counting Rule to Determine the Number of Possible Outcomes

• Define Combinations and the Factorial Operation

• Apply the Combinations Formula to Determine the Number of Possible Outcomes

• Contrast the Situations where It Is Appropriate to Use Combinations and Permutat

• Contrast Situations where It Is Appropriate to Count Combinations & Permutations

• Contrast P(A ∪ B) and P(A ∩ B)

• Use the Addition Rule of Probability with and without a Contingency Table

• Contrast the Meaning of Mutually Exclusive Events and Independent Events

• Use the Addition Rule of Probability for Mutually Exclusive Events

• Interpret a Conditional Probability

• Use the Conditional Rule of Probability Without a Contingency Table

• Use the Conditional Rule of Probability With a Contingency Table

• Use the Multiplication Rule for Independent Events

• Use the Multiplication Rule for Dependent Events

• Know the Approach to Calculate the Probability of At Least One of Something

• Calculate the Probability of At Least One of Something

• Mixed Practice Section 3

• Probability Distributions for Discrete Random Variables

• Calculate and Interpret the Expected Value of a Discrete Random Variable

• Calculate the Variance and Standard Deviation of a Discrete Random Variable

• The Characteristics of a Binomial Experiment & the Binomial Probability Formula

• Calculate the Probability of X Successes in a Binomial Experiment

• Calculate the Probability of a Cumulative Set of Events for a Binomial Experimen

• Calculate the Mean and Standard Deviation of a Binomial Random Variable

• Mixed Practice Section 3 and 4

• Traits of Continuous Random Variables

• Contrast Probability for Continuous Random Variables & Discrete Random Variables

• A Family of Normal Distributions

• Find Areas Under the Standard Normal Curve between the Mean and a Value

• Areas Under the Standard Normal Curve Inside an Interval Surrounding the Mean

• Areas Under the Normal Curve between Two Values on the Same Side of the Mean

• Areas Under the Standard Normal Curve between a Positive Z Value and Infinity

• Areas Under the Standard Normal Curve between a Negative Z Value and Infinity

• Calculate a Tail Area for a Non-Standard Normal Random Variable

• Calculate the Probability a Normal Random Variable is Above-Average or Less

• Probability a Normal Random Variable is Between Values that Surround the Mean

• Calculate the Probability a Normal Variable is Between Two Above Average Values

• Calculate the Probability a Normal Variable is Between Two Below Average Values

• Calculate the Value Corresponding to an Upper Percentile of the Normal Curve

• Calculate the Value Corresponding to a Lower Percentile of the Normal Curve

• Mixed Practice Section 5

• Sampling Distributions and the Desired Traits of a Point Estimator

• The Mean and Standard Error of the Sample Mean

• The Central Limit Theorem

• Applying the Central Limit Theorem

• Mixed Practice Sections 5 and 6

• Interval Estimators

• Finding Critical Z Values

• Constructing a Large Sample Confidence Interval to Estimate a Mean

• Determine the Sample Size Needed to Estimate a Mean

• Finding Critical t Values

• Constructing a Small Sample Confidence Interval to Estimate a Mean

• The Sampling Distribution of the Sample Proportion

• Constructing a Confidence Interval for the Population Proportion

• Mixed Review for Section 7

• Properties of the Null and Alternative Hypotheses

• Determine the Null and Alternative Hypothesis

• Test Statistics

• Type I and Type II Errors

• Reducing the Likelihood of a Type I Error

• Finding a Critical Value for a One-Tailed Hypothesis Test

• Express the Rejection Region for a Two-Tailed Hypothesis Test

• The Classical Approach to a Large-Sample Hypothesis Test of the Population Mean

• Lecture 91.1 The liklihood of a Type I Error

• Rules for Calculating a P-Value

• Calculating a P-Value

• The P-Value Method of Hypothesis Testing

• Finding a t Critical Value for a Two-Tailed Hypothesis Test

• Small-Sample Hypothesis Tests about a Population Mean

• Mixed Practice Sections 7 and 8