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1
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Statistics: An Introduction and Basic Concepts
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- Use of Statistics
- Types of Variables
- Levels of Measurement
- Ethics in Statistics
- Software and Statistics
- Graphical Displays of Categorical Data
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- Differentiate between the word “statistics” and the science of statistics.
- Describe the importance of statistics and situations where statistics are used in business and everyday life; identify business situations in which statistics can be used appropriately and inappropriately.
- Identify qualitative versus quantitative and discrete versus continuous variables.
- Discuss the levels of measurement and choose the most appropriate level of measurement for a specified situation.
- Explain the role of computer software in statistical analysis and identify some of the most popular software packages.
- Construct bar charts to display categorical data.
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2
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Descriptive Statistics: Numerical Measures
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- Arithmetic Mean
- Geometric Mean
- Median and Mode
- Measures of Dispersion
- Chebyshev's Theorem and the Empirical Rule
- Using Software to Compute Descriptive Statistics
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- Calculate the arithmetic mean for a given set of data.
- Calculate the geometric mean for a given set of data.
- Calculate the median and mode for a given set of data.
- Compute and interpret the range, mean deviation, variance, and standard deviation for data observations.
- Interpret data using Chebyshev's theorem and the Empirical rule.
- Understand how software can be used in computing various measures of location and dispersion.
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3
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Descriptive Statistics: Representational
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- Dot Plot, Stem Plot and Histogram
- Quartiles, Deciles, and Percentiles
- Skewness
- Bivariate Data
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- Create and interpret dot plot, box plot, and scatter diagrams.
- Define and compute quartiles, deciles, and percentiles.
- Compute and interpret the coefficient of skewness.
- Construct a contingency table.
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4
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Probability
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- Probability Approaches
- Probability Calculations
- Tools of Analysis
- Computing the Number of Possible Outcomes
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- Discuss the objective and subjective approaches to probability analysis.
- Calculate probability using the rules of addition and multiplication.
- Use and interpret contingency tables, Venn diagrams, and tree diagrams.
- Compute the number of possible outcomes for combinations and permutations using formulae and Excel functions.
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5
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Discrete and Continuous Probability Distributions
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- Discrete Probability Distributions
- Binomial Probability Distributions
- Poisson Probability Distributions
- Uniform Probability Distributions
- Normal Probability Distributions
- Sampling Distribution of the Sample Mean
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- Explain the difference between discrete and continuous distribution.
- Compute the mean and the standard deviation for a uniform distribution.
- Calculate the mean, variance, and standard deviation of a probability distribution.
- Compute probabilities using the binomial probability distribution.
- Compute probabilities using the uniform distribution.
- Calculate areas under a normal curve using the Empirical Rule.
- Compute probabilities using the Poisson probability distribution.
- Compute probabilities using the normal probability distribution.
- Select a sample and construct a sampling distribution of the mean.
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6
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Sampling Methods and the Central Limit Theory
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- Sampling a Population
- Sampling Errors
- Central Limit Theorem
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- Define the terms population and sample.
- Explain the need for sampling.
- Use a simple random sampling technique to select members of the general populate.
- Understand more complex sampling techniques, such as stratified, cluster, and systematic random sampling.
- Identify sampling errors in a given situation.
- Explain the importance of the central limit theorem and how it applies to sample distributions.
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7
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Using Confidence Intervals in the Sampling Process
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- Large Sample Confidence Intervals
- Small Sample Confidence Intervals
- Proportions
- Sample Size
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- Define the terms confidence interval, point estimate, and degrees of freedom, and explain how they are involved in the sampling process.
- Demonstrate the ability to compute a confidence interval for a large sample experiment.
- Compute a confidence interval for a small sample experiment.
- Compute a confidence interval for a proportion.
- Determine an appropriate sample size for small, large, and proportion experiments.
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8
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Tests of Hypothesis
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- Hypothesis Testing: An Introduction
- Decision Making in Hypothesis Testing
- Hypothesis Testing with Proportions
- Two-Sample Test of Hypothesis
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- Formulate null and alternate hypotheses, and test the hypothesis using the five steps of the hypothesis testing procedure.
- Discuss Type I and Type II errors on a test of hypothesis.
- Perform a one-tailed and a two-tailed test of hypothesis.
- Perform a test of hypothesis on the difference between two population means using the z and t statistics.
- Perform a test of hypothesis on a population proportion using the z statistic.
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9
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Analysis of Variance
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- Using the F Distribution in Variance Analysis
- Analysis of Variance (ANOVA)
- Computing the Analysis of Variance (ANOVA) - Sum of Squares
- Analyzing the Variance
- Use of Software in Variance Analysis
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- Discuss the general idea of analysis of variance and analyze the given F distribution.
- Test a hypothesis to determine whether the variances of two populations are equal.
- Test a hypothesis about three or more treatment means and develop confidence intervals for the difference between treatment means.
- Perform an analysis of variance (ANOVA).
- Understand how to use statistical software in variance analysis.
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10
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Regression Analysis
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- Correlation Analysis
- Coefficient of Correlation
- Regression Analysis
- Confidence Interval and Prediction Intervals
- ANOVA Table
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- Discuss the difference between correlation and causation.
- Analyze the correlation between two variables in specified situations.
- Calculate and interpret the coefficient of correlation, the coefficient of determination, and the standard error.
- Calculate and interpret the linear regression line.
- Construct and interpret a confidence interval and prediction interval for a dependent variable.
- Use an ANOVA table data to compute statistics.
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11
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Multiple Regression Analysis
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- Multiple Regression Analysis Equation
- Analyzing ANOVA Table Output
- Analyzing Individual Independent Variables
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- Analyze the relationships between several independent variables and a dependent variable.
- Test to determine whether the regression coefficient for each independent (or explanatory) variable has a significant influence on the dependent variable.
- Calculate and interpret multiple regression analysis.
- Compute variance of regression using the standard error of estimate and the ANOVA table.
- Calculate and interpret the coefficient of determination and the correlation matrix.
- Identify the violation of assumptions: homoscedasticity and autocorrelation.
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12
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Nonparametric Methods
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- Chi-Square Test
- Contingency Table Analysis
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- Test a hypothesis comparing an observed set of frequencies to an expected set of frequencies using the chi-square test.
- Identify the limitation of the chi-square test in a specified situation.
- Analyze relationships in statistical data using a contingency table.
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13
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Process Improvement Techniques
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- Statistical Process Control
- Creating Control Charts
- Analyzing Control Charts
- Natural Tolerance Limits
- p Chart
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- Identify the causes of process variation and apply statistical process control to reduce process variation.
- Sample a process and use rational sub-grouping to control process.
- Use statistical software to create X-bar and R-charts.
- Interpret information presented in control charts and R-charts to identify assignable causes and analyze patterns.
- Calculate and analyze the upper and lower natural tolerance limits to evaluate whether a process is capable of meeting specifications.
- Construct p chart for fraction nonconforming.
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