MAT1140: Introduction to Statistics
- Page ID
- 28061
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)- 1: Sampling and Data
- Included in this chapter are the basic ideas and words of probability and statistics. You will soon understand that statistics and probability work together. You will also learn how data are gathered and what "good" data can be distinguished from "bad."
- 2: Descriptive Statistics
- In this chapter, you will study numerical and graphical ways to describe and display your data. This area of statistics is called "Descriptive Statistics." You will learn how to calculate, and even more importantly, how to interpret these measurements and graphs.
- 2.1: Prelude to Descriptive Statistics
- 2.2: Frequency, Frequency Tables, and Levels of Measurement
- 2.3: Stem-and-Leaf Graphs (Stemplots), Line Graphs, and Bar Graphs
- 2.4: Histograms, Frequency Polygons, and Time Series Graphs
- 2.5: Measures of the Location of the Data
- 2.6: Box Plots
- 2.7: Measures of the Center of the Data
- 2.8: Skewness and the Mean, Median, and Mode
- 2.9: Measures of the Spread of the Data
- 2.10: Descriptive Statistics (Worksheet)
- 2.E: Descriptive Statistics (Exercises)
- 3: Discrete Random Variables
- 3.1: Prelude to Discrete Random Variables
- 3.2: Probability Distribution Function (PDF) for a Discrete Random Variable
- 3.3: Mean or Expected Value and Standard Deviation
- 3.4: Binomial Distribution
- 3.5: Geometric Distribution
- 3.6: Discrete Distribution (Playing Card Experiment)
- 3.7: Discrete Distribution (Lucky Dice Experiment)
- 3.E: Discrete Random Variables (Exercises)
- 4: The Normal Distribution
- In this chapter, you will study the normal distribution, the standard normal distribution, and applications associated with them. The normal distribution has two parameters (two numerical descriptive measures), the mean ( μμ ) and the standard deviation ( σσ ).
- 5: The Central Limit Theorem
- In a population whose distribution may be known or unknown, if the size (n) of samples is sufficiently large, the distribution of the sample means will be approximately normal. The mean of the sample means will equal the population mean. The standard deviation of the distribution of the sample means, called the standard error of the mean, is equal to the population standard deviation divided by the square root of the sample size (n).
- 5.1: Prelude to the Central Limit Theorem
- 5.2: The Central Limit Theorem for Sample Means (Averages)
- 5.3: The Central Limit Theorem for Sums
- 5.4: Using the Central Limit Theorem
- 5.5: Central Limit Theorem - Pocket Change (Worksheet)
- 5.6: Central Limit Theorem - Cookie Recipes (Worksheet)
- 5.E: The Central Limit Theorem (Exercises)
- 6: Confidence Intervals
- In this chapter, you will learn to construct and interpret confidence intervals. You will also learn a new distribution, the Student's-t, and how it is used with these intervals. Throughout the chapter, it is important to keep in mind that the confidence interval is a random variable. It is the population parameter that is fixed.
- 6.1: Prelude to Confidence Intervals
- 6.2: A Single Population Mean using the Normal Distribution
- 6.3: A Single Population Mean using the Student t-Distribution
- 6.4: A Population Proportion
- 6.5: Confidence Interval - Home Costs (Worksheet)
- 6.6: Confidence Interval -Place of Birth (Worksheet)
- 6.7: Confidence Interval -Women's Heights (Worksheet)
- 6.E: Confidence Intervals (Exercises)
- 6.S: Confidence Intervals (Summary)
- 7: Hypothesis Testing with One Sample
- 7.1: Prelude to Hypothesis Testing
- 7.2: Null and Alternative Hypotheses
- 7.3: Outcomes and the Type I and Type II Errors
- 7.4: Distribution Needed for Hypothesis Testing
- 7.5: Rare Events, the Sample, Decision and Conclusion
- 7.6: Additional Information and Full Hypothesis Test Examples
- 7.7: Hypothesis Testing of a Single Mean and Single Proportion (Worksheet)
- 7.8: Test of a Single Variance
- 7.E: Hypothesis Testing with One Sample (Exercises)
- 8: Hypothesis Testing with Two Samples
- You have learned to conduct hypothesis tests on single means and single proportions. You will expand upon that in this chapter. You will compare two means or two proportions to each other. To compare two means or two proportions, you work with two groups. The groups are classified either as independent or matched pairs.
- 8.1: Prelude to Hypothesis Testing with Two Samples
- 8.2: Two Population Means with Unknown Standard Deviations
- 8.3: Two Population Means with Known Standard Deviations
- 8.4: Comparing Two Independent Population Proportions
- 8.5: Matched or Paired Samples
- 8.6: Hypothesis Testing for Two Means and Two Proportions (Worksheet)
- 8.E: Hypothesis Testing with Two Samples (Exercises)
- 9: Linear Regression and Correlation
- Regression analysis is a statistical process for estimating the relationships among variables and includes many techniques for modeling and analyzing several variables. When the focus is on the relationship between a dependent variable and one or more independent variables.
- 9.1: Prelude to Linear Regression and Correlation
- 9.2: Linear Equations
- 9.3: Scatter Plots
- 9.4: The Regression Equation
- 9.5: Testing the Significance of the Correlation Coefficient
- 9.6: Prediction
- 9.7: Outliers
- 9.8: Regression - Distance from School (Worksheet)
- 9.9: Regression - Textbook Cost (Worksheet)
- 9.10: Regression - Fuel Efficiency (Worksheet)
- 9.E: Linear Regression and Correlation (Exercises)