1

Statistics: An Introduction and Basic Concepts

 Use of Statistics
 Types of Variables
 Levels of Measurement
 Ethics in Statistics
 Software and Statistics
 Graphical Displays of Categorical Data

 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.

2

Descriptive Statistics: Numerical Measures

 Arithmetic Mean
 Geometric Mean
 Median and Mode
 Measures of Dispersion
 Chebyshev's Theorem and the Empirical Rule
 Using Software to Compute Descriptive Statistics

 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.

3

Descriptive Statistics: Representational

 Dot Plot, Stem Plot and Histogram
 Quartiles, Deciles, and Percentiles
 Skewness
 Bivariate Data

 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.

4

Probability

 Probability Approaches
 Probability Calculations
 Tools of Analysis
 Computing the Number of Possible Outcomes

 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.

5

Discrete and Continuous Probability Distributions

 Discrete Probability Distributions
 Binomial Probability Distributions
 Poisson Probability Distributions
 Uniform Probability Distributions
 Normal Probability Distributions
 Sampling Distribution of the Sample Mean

 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.

6

Sampling Methods and the Central Limit Theory

 Sampling a Population
 Sampling Errors
 Central Limit Theorem

 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.

7

Using Confidence Intervals in the Sampling Process

 Large Sample Confidence Intervals
 Small Sample Confidence Intervals
 Proportions
 Sample Size

 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.

8

Tests of Hypothesis

 Hypothesis Testing: An Introduction
 Decision Making in Hypothesis Testing
 Hypothesis Testing with Proportions
 TwoSample Test of Hypothesis

 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 onetailed and a twotailed 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.

9

Analysis of Variance

 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

 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.

10

Regression Analysis

 Correlation Analysis
 Coefficient of Correlation
 Regression Analysis
 Confidence Interval and Prediction Intervals
 ANOVA Table

 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.

11

Multiple Regression Analysis

 Multiple Regression Analysis Equation
 Analyzing ANOVA Table Output
 Analyzing Individual Independent Variables

 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.

12

Nonparametric Methods

 ChiSquare Test
 Contingency Table Analysis

 Test a hypothesis comparing an observed set of frequencies to an expected set of frequencies using the chisquare test.
 Identify the limitation of the chisquare test in a specified situation.
 Analyze relationships in statistical data using a contingency table.

13

Process Improvement Techniques

 Statistical Process Control
 Creating Control Charts
 Analyzing Control Charts
 Natural Tolerance Limits
 p Chart

 Identify the causes of process variation and apply statistical process control to reduce process variation.
 Sample a process and use rational subgrouping to control process.
 Use statistical software to create Xbar and Rcharts.
 Interpret information presented in control charts and Rcharts 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.
