This course will begin with a brief overview of the discipline of statistics and will then quickly focus on descriptive statistics, introducing graphical methods of describing data. You will learn about combinatorial probability and random distributions, the latter of which serves as the foundation for statistical inference. On the side of inference, we will focus on both estimation and hypothesis testing issues. We will also examine the techniques to study the relationship between two or more variables; this is known as regression. By the end of this course, you should gain a sound understanding about what statistics represent, how to use statistics to organize and display data, and how to draw valid inferences based on data by using appropriate statistical tools.

### Unit 1: Statistics and Da...

Upon successful completion of this unit, you will be able to: describe various types of sampling methods to data collection, and apply these methods; create and interpret frequency tables; display data graphically and interpret the following types of graphs: stem plots, histograms, and boxplots; identify, describe, and calculate the following measures of the location of data: quartiles and percentiles; identify, describe, and calculate the measures of the center of mean, median, and mode; and identify, describe, and calculate the following measures of the spread of data: variance, standard deviation, and range.

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Review and intuition why we divide by n-1 for the ...

# Review and intuition why we divide by n-1 for the unbiased sample

### Unit 2: Elements of Proba...

apply simple principles of probability, and use common terminology of probability; calculate conditional probability, and determine whether two events are mutually exclusive and whether two events are independent; calculate probabilities using the addition rules and multiplication rules; construct and interpret Venn diagrams; apply useful counting rules in the context of combinatorial probability; identify and use common discrete probability distribution functions; calculate and interpret expected values; identify the binomial probability distribution, and apply it appropriately; identify the Poisson probability distribution, and apply it appropriately; identify and use continuous probability density functions; and identify the normal probability distribution, and apply it appropriately.

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Free throw binomial probability distribution

# Free throw binomial probability distribution

### Unit 3: Sampling Distribu...

apply the central limit theorem to approximate sampling distributions; describe the role of sampling distributions in inferential statistics; interpret and create graphs of a probability distribution for the mean of a discrete variable; describe a sampling distribution in terms of repeated sampling; define and compute the mean and standard deviation of the sampling distribution of population proportion p; identify or approximate a sampling distribution based on the properties of the population; compare and evaluate the sampling distributions of different sample sizes; and compare and evaluate the performance of different estimators based on their sampling distributions.

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### Unit 4: Estimation with C...

explain the central limit theorem, and use it to construct confidence intervals; compare t-distributions and normal distributions; apply and interpret the central limit theorem for sample averages; calculate, describe, and interpret confidence intervals for population averages and one population proportions; and interpret the student-t probability distribution as the sample size changes.

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### Unit 5: Hypothesis Test

differentiate between type I and type II errors, and find the probability of these errors; describe and conduct hypothesis testing, calculate the p-value, and accept or reject the null hypothesis; and explain how to conduct hypothesis tests for a single population mean and population proportion, when the population standard deviation is unknown; perform this task; and interpret the results.

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### Unit 6: Linear Regression

discuss and apply basic ideas of linear regression and correlation; identify the assumptions that inferential statistics in regression are based on; compute the standard error of a slope; test a slope for significance; construct a confidence interval on a slope; and calculate and interpret the coefficient of determination and the correlation coefficient.

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