This course from Saylor.org introduces the fundamental concepts of statistics. The course description provided by Saylor.org is as followed: In this course, you will look at the properties behind the basic concepts of probability and statistics and focus on applications of statistical knowledge. You will learn about how statistics and probability work together. The subject of statistics involves the study of methods for collecting, summarizing, and interpreting data. Statistics formalizes the process of making decisions, and this course is designed to help you use statistical literacy to make better decisions.

### Unit 1: Data and Descript...

Unit description from Saylor.org: In today's world we access and use large volumes of data every day. The first step of data analysis is to accurately summarize this data, both graphically and numerically, so that we can understand what the data is saying. To be able to use and interpret data correctly is essential to making informed decisions. In this unit you will learn about descriptive statistics, which is used to summarize and display data. After completing this unit, you will know what you can do to present data that you have collected.

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### Unit 2: Probability Topic...

Unit Description from Saylor.org: After you have learned to describe and display data, how can you use the sample data to draw conclusions about the populations? To answer this question, you need probability, a subject we will explore over the course of this unit.

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### Unit 3: Random Variables ...

Description from Saylor.org: In the last unit, you learned how to calculate probabilities in the framework of sample spaces, outcomes, and events. In this unit, you will build on those ideas and learn about random variables. A random variable describes the outcomes of a statistical experiment. A statistical distribution describes the numbers of times each possible outcome occurs in a sample. The values of a random variable can vary with each repetition of an experiment. Intuitively, a random variable is an observable that takes on values with certain probabilities.

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### Unit 4: Central Limit The...

The unit description from Saylor.org: In this unit, you will learn how to use the central limit theorem and confidence intervals, the latter of which enable us to estimate unknown population parameters. The central limit theorem provides us a way to make inference from samples of non-normal populations. This theorem states that given any population (regardless of whether or not it is a normal distribution), as the sample size increases, the sampling distribution of the means approaches a normal distribution. It is a powerful theorem because it allows us to assume that given a large enough sample, the sampling distribution will be normally distributed. The central limit theorem is one of the most important ideas in statistics, so be sure to spend time on it.

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Sampling distribution of the sample mean 2

# Sampling distribution of the sample mean 2

### Unit 5: Hypothesis Testin...

The unit description from Saylor.org: One of the major goals in statistics is to use the information you collect from a sample to get a better idea of the entire population in which you are interested. In this unit, you will learn about hypothesis testing, which will enable you to achieve that goal. A hypothesis test involves collecting and evaluating data from a sample to make a decision as to whether or not that data supports a claim made about a population. This unit will also teach you how to conduct hypothesis tests and to identify and differentiate between the errors associated with them.

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Large Sample Proportion Hypothesis Testing

# Large Sample Proportion Hypothesis Testing

Hypothesis Test Comparing Population Proportions

# Hypothesis Test Comparing Population Proportions

Pearson's Chi Square Test (Goodness of Fit)

# Pearson's Chi Square Test (Goodness of Fit)

### Unit 6: Correlation, Regr...

The unit description from Saylor.org: One of the main reasons you will conduct analysis is in order to understand how two variables are related to one another. The most common type of relationship is a linear relationship... Correlation quantifies the strength of a relationship between two variables and is a measure of existing data. Regression, on the other hand, is the study of the strength of a linear relationship between an independent and dependent variable, and can be used to predict the value of the dependent variable when the value of the independent variable is unknown. Also, you will learn about a method called Analysis of Variance (abbreviated ANOVA), which is used for hypothesis tests involving more than two averages. ANOVA is about examining the amount of variability in the Y variable and trying to see where that variability is coming from.

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