Math 120 Probability and Statistics

Topic Video Notes
Basic Probability Video Notes
Binomial and Normal Distributions Video Notes

Course Videos

Each of these links send you to a play list of the videos for that chapter. The videos are listed both by section number and topic.

Chapter 1 — This chapter covers:

  • Define Statistics and statistical thinking
  • Explain the process of statistics
  • Distinguish between qualitative and quantitative variables
  • Distinguish between discrete and continuous variables
  • Determine the level of measurement of a variable
  • Distinguish between an observational study and an experiment
  • Explain the various types of observational studies
  • Obtain a simple random sample
  • Obtain a stratified sample
  • Obtain a systematic sample
  • Obtain a cluster sample
  • Explain the sources of bias in sampling
  • Describe the characteristics of an experiment

Chapter 2 — This chapter covers:

  • Organize qualitative data in tables
  • Construct bar graphs
  • Construct pie charts
  • Organize discrete data in tables
  • Construct histograms of discrete data
  • Organize continuous data in tables
  • Construct histograms of continuous data
  • Draw stem-and-leaf plots
  • Identify the shape of a distribution
  • Construct frequency polygons
  • Create cumulative frequency and relative frequency tables
  • Construct frequency and relative frequency ogives
  • Draw time-series graphs
  • Describe what can make a graph misleading or deceptive

Chapter 3 — This chapter covers:

  • Determine the arithmetic mean of a variable from raw data
  • Determine the median of a variable from raw data
  • Explain what it means for a statistic to be resistant
  • Determine the mode of a variable from raw data
  • Determine the range of a variable from raw data
  • Determine the standard deviation of a variable from raw data
  • Determine the variance of a variable from raw data
  • Use the Empirical Rule to describe data that are bell shaped
  • Use Chebyshev’s Inequality to describe any set of data
  • Approximate the mean of a variable from grouped data
  • Compute the weighted mean
  • Approximate the standard deviation of a variable from grouped data
  • Determine and interpret z-scores
  • Interpret percentiles
  • Determine and interpret quartiles
  • Determine and interpret the interquartile range
  • Check a set of data for outliers
  • Compute the five-number summary
  • Draw and interpret boxplots

Chapter 4 — This chapter covers:

  • Draw and interpret scatter diagrams
  • Describe the properties of the linear correlation coefficient
  • Compute and interpret the linear correlation coefficient
  • Determine whether a linear relation exists between two variables
  • Explain the difference between correlation and causation
  • Find the lest-squares regression line and use the line to make predictions
  • Interpret the slope and the y-intercept of the least-squares regression line
  • Compute the sum of squared residuals
  • Compute and determine the coefficient of determination
  • Perform residual analysis on a regression model
  • Identify influential observations

Chapter 5 — This chapter covers:

  • Apply the rules of probabilities
  • Compute and interpret probabilities using the empirical method
  • Compute and interpret probabilities using the classical method
  • Recognize and interpret subjective probabilities
  • Use the Addition Rule for disjoint events
  • Use the General Addition Rule
  • Compute the probability of an event using the
  • Complement Rule
  • Identify independent events
  • Use the Multiplication Rule for independent events
  • Compute at-least probabilities
  • Compute conditional probabilities
  • Compute probabilities using the General Multiplication Rule
  • Solve counting problems using the Multiplication Rule
  • Solve counting problems using permutations
  • Solve counting problems using combinations
  • Solve counting problems involving permutations with non-distinct items
  • Compute probabilities involving permutations and combinations.
  • Determine the appropriate probability rule to use
  • Determine the appropriate counting technique to use

Chapter 6 — This chapter covers:

  • Distinguish between discrete and continuous random variables
  • Identify discrete probability distributions
  • Construct probability histograms
  • Compute and interpret the mean of a discrete random variable
  • Interpret the mean of a discrete random variable as an expected value
  • Compute the standard deviation of a discrete random variable
  • Determine whether a probability experiment is a binomial experiment
  • Compute probabilities of binomial experiments
  • Compute the mean and standard deviation of a binomial random variable
  • Construct binomial probability histograms

Chapter 7 — This chapter covers:

  • Use the uniform probability distribution
  • Graph a normal curve
  • State the properties of the normal curve
  • Explain the role of area in the normal density function
  • Find and interpret the area under a normal curve
  • Find the value of a normal random variable

Chapter 8 — This chapter covers:

  • Describe the distribution of the sample mean: normal population
  • Describe the distribution of the sample mean: non-normal population
  • Describe the sampling distribution of a sample proportion
  • Compute probabilities of a sample proportion

Chapter 9 — This chapter covers:

  • Obtain a point estimate for the population proportion
  • Construct and interpret a confidence interval for the population proportion
  • Determine the sample size necessary for estimating a population proportion within a specified margin of error
  • Obtain a point estimate for the population mean
  • State properties of Student’s t-distribution
  • Determine t-values
  • Construct and interpret a confidence interval for a population mean
  • Find the sample size needed to estimate the population mean within a given margin of error
  • Find critical values for the chi-square distribution
  • Construct and interpret confidence intervals for the population variance and standard deviation
  • Determine the appropriate confidence interval to construct

Chapter 10 — This chapter covers:

  • Determine the null and alternative hypotheses
  • Explain Type I and Type II errors
  • State conclusions to hypothesis tests
  • Explain the logic of hypothesis testing
  • Test hypotheses about a population proportion
  • Test hypotheses about a population proportion using the binomial probability distribution
  • Test hypotheses about a mean
  • Understand the difference between statistical significance and practical significance
  • Test hypotheses about a population standard deviation
  • Determine the appropriate hypothesis test to perform

Chapter 11 — This chapter covers:

  • Distinguish between independent and dependent sampling
  • Test hypotheses regarding two proportions from independent samples
  • Construct and interpret confidence intervals for the difference between two population proportions.
  • Determine the sample size necessary for estimating the difference between two population Proportions
  • Test hypotheses regarding matched-pairs data
  • Construct and interpret confidence intervals about the population mean difference of matched-pairs data
  • Test hypotheses regarding the difference of two independent means
  • Construct and interpret confidence intervals regarding the difference of two independent means
  • Find critical values of the F-distribution
  • Test hypotheses regarding two population standard deviations
  • Determine the appropriate hypothesis test to perform

Chapter 12 — This chapter covers:

  • Perform a goodness-of-fit test
  • Perform a test for independence
  • Perform a test for homogeneity of proportions

Chapter 13 — This chapter covers:

  • Verify the requirements to perform a one-way ANOVA
  • Test a hypothesis regarding three or more means using one-way ANOVA

Chapter 14 — This chapter covers:

  • State the requirements of the least-squares regression model
  • Compute the standard error of the estimate
  • Verify that the residuals are normally distributed
  • Conduct inference on the slope
  • Construct a confidence interval about the slope of the least-squares regression model
  • Construct confidence intervals for a mean response

Chapter 15 — This chapter covers:

  • Distinguish between parametric and non parametric statistical procedures
  • Inference about measures of central tendency