Course | Madison College Outline of Instruction

20804241Introduction to Engineering Statistics

Course Information

Description

This is an introductory course with many examples and applications chosen from the engineering disciplines and physical science. The course covers techniques for the collection, presentation, analysis and interpretation of experimental results and develops procedures to deal with the uncertainty present in making inferences and decisions based on sample data. Topics covered include descriptive statistics; probability concepts, random variables and discrete probability distributions; continuous probability and sampling distributions, the Central Limit Theorem; hypothesis tests and confidence intervals for one- and two-sample problems; one-way analysis of variance and basic ideas in experimental design; linear regression, model checking, and inference.

Total Credits

Course Competencies

Interpret Basic Statistical Terminology.

Assessment Strategies

in the solution to a problem on a quiz, homework, project or exam

Criteria

you distinguish between a sample and a population

you distinguish between a sample statistic and a population parameter
Generate Frequency Distributions.

Assessment Strategies

in the solution to a problem on a quiz, homework, project or exam

Criteria

you generate a frequency distribution from a given data set

you group a frequency distribution into classes

you calculate the frequency, relative frequency, and cumulative frequency of each class

you calculate the width and midpoint of each class

you interpret the frequency, relative frequency and cumulative frequency of each class

you use technology to generate a frequency distribution
Generate Graphical Representations of Data.

Assessment Strategies

in the solution to a problem on a quiz, homework, project or exam

Criteria

you generate an x-bar chart showing a time series of sample averages

you interpret an x-bar chart showing a time series of sample averages

you generate a Pareto diagram and its corresponding cumulative frequency distribution

you interpret a Pareto diagram and its corresponding cumulative frequency distribution or Ogive

you generate a dot diagram

you interpret a dot diagram

you generate a stem-and-leaf display

you interpret a stem-and-leaf display

you generate histograms of frequency distributions

you interpret histograms of frequency distributions

you generate a box plot from a frequency distribution

you interpret a box plot from a frequency distribution

you analyze a box plot for outliers

you use a histogram or box plot to estimate measures of central tendency and dispersion

you demonstrate the connections between information found in a histogram or a box plot and calculated descriptive statistics

you use technology to generate graphical representations of data
Calculate Descriptive Measures of a frequency distribution.

Assessment Strategies

in the solution to a problem on a quiz, homework, project or exam

Criteria

you calculate the mode of a frequency distribution

you interpret the mode of a frequency distribution

you calculate the mean of a frequency distribution

you interpret the mean of a frequency distribution

you calculate the median of a frequency distribution

you interpret the median of a frequency distribution

you calculate the quartiles of a frequency distribution

you interpret the quartiles of a frequency distribution

you calculate the percentile scores of a frequency distribution

you interpret the percentile scores of a frequency distribution

you calculate inter-quartile range of a frequency distribution

you interpret the inter-quartile range of a frequency distribution

you calculate the range of a frequency distribution

you interpret the range of a frequency distribution

you calculate the variance of a frequency distribution

you interpret the variance of a frequency distribution

you calculate the standard deviation of a frequency distribution

you interpret the standard deviation of a frequency distribution

you demonstrate the relationship between the variance and standard deviation

you distinguish the population standard deviation from the sample standard deviation

you use the properties of the mean and standard deviation

you calculate the coefficient of variation of a frequency distribution

you interpret the coefficient of variation of a frequency distribution

you calculate z scores for a frequency distribution

you interpret z scores for a frequency distribution

you use the properties of z scores

you demonstrate the connections between z scores and the properties of the mean

you demonstrate the connections between z scores and the properties of standard deviation

you use both Chebyshev's inequality and the percentage points for a normal distribution to estimate the fraction of scores beyond a given z score

you use technology to calculate the descriptive statistics of a frequency distribution
Use the Definitions and Axioms of Probability.

Assessment Strategies

in the solution to a problem on a quiz, homework, project or exam

Criteria

you distinguish between theoretical and empirical probabilities

you generate a representation of a sample space of an experiment by listing all outcomes, drawing Venn diagrams, making tree diagrams, or constructing tables

you use a representation of the sample space of an experiment and the fair experiment or equi-probability model to compute probabilities

you use the fundamental rule of counting, the number of permutations, the number of combinations, and binomial coefficients to compute the number of outcomes in a given event

you recognize computations which count the number of outcomes corresponding to a given event

you formulate and evaluate computations which count the number of outcomes corresponding to a given event

you use counting rules to compute event probabilities

you use set theory rules to calculate the probability of unions, intersections, and complements of events

you distinguish mutually exclusive events from events with non-null intersection

you recognize conditional probabilities

you formulate and evaluate conditional probabilities

you use and interpret Bayes' Theorem for calculating conditional probabilities

you determine if two events are independent

you compare and contrast the intuitive notion of event independence from the formal definition

you distinguish between mutually exclusive and independent events

you recognize events that are neither independent nor mutually exclusive

you use a tree diagram to distinguish the probabilities of a false positive and a false negative test

you use a tree diagram to compute the probabilities of a false positive and a false negative test

you recognize computations which calculate the reliability of systems consisting of components arranged in series or parallel

you formulate and evaluate computations which calculate the reliability of systems consisting of components arranged in series or parallel
Use Probability Distributions of a Discrete Random Variable.

Assessment Strategies

in the solution to a problem on a quiz, homework, project or exam

Criteria

you generate the probability distribution of a discrete random variable

you generate histograms for the probability distribution of a discrete random variable

you interpret histograms for the probability distribution of a discrete random variable

you compute the mean of a discrete random variable

you compute the variance of a discrete random variable

you compute the standard deviation of a discrete random variable

you demonstrate the connections between the formulas for the mean, variance and standard deviation of a random variable

you demonstrate the connections between the formulas for the mean, variance and standard deviation of a random variable and those used in descriptive statistics

you distinguish a drawing without replacement from a drawing with replacement

you formulate and compute probabilities of events associated with random drawings

you recognize when the hypergeometric distribution applies to a drawing without replacement

you formulate and compute probabilities of events associated with the hypergeometric distribution

you recognize when an experiment is a succession of simple Bernoulli trials

you formulate and compute event probabilities for an experiment consisting of simple Bernoulli trials using the binomial distribution

you calculate the mean of a hypergeometric or binomial random variable

you calculate the variance of a hypergeometric or binomial random variable

you calculate the standard deviation of a hypergeometric or binomial random variable

you interpret the mean of a hypergeometric or binomial random variable

you interpret the variance of hypergeometric or binomial random variable

you interpret the standard deviation of a hypergeometric or binomial random variable

you demonstrate the connections between the formulas for the mean, variance and standard deviation of hypergeometric and binomial random variables and the corresponding formulas for a generic random variable

you demonstrate the connections between the formulas for the mean, variance and standard deviation of both hypergeometric and binomial distributions

you use the binomial distribution to approximate the hypergeometric distribution for large populations

you justify the validity of the binomial distribution to approximate the hypergeometric distribution for large populations

you state and interpret Chebyshev's Theorem and apply it to a large number of simple Bernoulli trials

you justify the "Law of Large Numbers" using Chebyshev's Theorem

you use the Poisson distribution to approximate a binomial distribution with large sample sizes and fixed mean number of successes

you justify why and when the Poisson distribution approximation is valid for a binomial distribution with large sample sizes and fixed mean number of successes

you use the geometric distribution to calculate the probability of a first success in a sequence of of simple Bernoulli trials

you calculate the mean of a geometric distribution

you use the multinomial distribution to analyze Bernoulli trials with multiple outcomes

you use technology to compute answers involving discrete probability distributions
Solve Applications Using Discrete Probability Distributions.

Assessment Strategies

in the solution to a problem on a quiz, homework, project or exam

Criteria

you use the concept of a fair experiment to model simple experiments such as coin or die tosses

you compare the theoretical and empirical probability distributions for a random variable associated with the simple experiments

you formulate and solve verbally stated applications which require using the hypergeometric, binomial, geometric, multinomial or Poisson distributions

you use probability distributions to analyze processes such as games of chance, insurance rates, instrument reliability and medical tests

you use fundamental counting rules and recursion to analyze models of simple experiments

you use technology to compare the theoretical and empirical probability distributions for a random variable associated with simple experiments
Apply the Properties of a Continuous Probability Distribution.

Assessment Strategies

in the solution to a problem on a quiz, homework, project or exam

Criteria

you distinguish between a continuous and a discrete random variable

you recognize the connection between the area under a probability density curve and the probability of an event

you recognize the connection between the definite integral of a probability density function and the probability of an event

you formulate a definite integral of a probability density function to calculate the probability of an event

you formulate a definite integral involving the probability density function to calculate the mean of a probability distribution

you formulate a definite integral involving the probability density function to calculate the variance of a probability distribution

you calculate event probabilities for a random variable with a uniform distribution

you relate the mean and standard deviation of a uniform distribution to its parameters

you estimate the mean of a continuous probability distribution from the graph of its probability density curve

you estimate the standard deviation of a continuous probability distribution from the graph of its probability density curve
Apply the Normal Distribution.

Assessment Strategies

in the solution to a problem on a quiz, homework, project or exam

Criteria

you use the normal distribution to approximate the binomial distribution for large sample sizes and a fixed probability of success

you justify why and when the normal distribution approximation is valid for the binomial distribution for large sample sizes and a fixed probability of success

you compute the area between two scores in a normal distribution by transforming to z scores and using the standard normal distribution

you determine critical z scores of a standard normal distribution from a stated probability

you use the probability density function of the standard normal distribution to generate a power series which computes standard normal probabilities

you use integration by parts to obtain an asymptotic approximation to a standard normal probability

you formulate and solve verbally stated applications which involve using the normal distribution

you generate a normal scores plot to check if scores are approximately normally distributed

you transform data to better approximate a problem with a normal distribution

you use technology to compute normal probabilities
Apply Other Continuous Probability Distributions.

Assessment Strategies

in the solution to a problem on a quiz, homework, project or exam

Criteria

you calculate event probabilities of a log-normal distribution

you relate the mean and standard deviation of a log-normal distribution to its parameters

you calculate event probabilities of a gamma distribution

you relate the mean and standard deviation of a gamma distribution to its parameters

you recognize the exponential distribution as a special case of the gamma distribution

you recognize the chi-squared distribution as a special case of the gamma distribution

you determine critical scores of a chi-squared distribution from a stated probability

you relate the mean and standard deviation of a chi-squared distribution to the degrees of freedom

you calculate event probabilities of a beta distribution

you relate the mean and standard deviation of a beta distribution to its parameters

you calculate event probabilities of a Weibull distribution

you relate the mean and standard deviation of a Weibull distribution to its parameters
Apply Joint Probability Distributions of Multiple Variables

Assessment Strategies

in the solution to a problem on a quiz, homework, project or exam

Criteria

you verify that a function of multiple discrete random variables is a valid joint probability distribution

you construct the marginal or individual probability distributions for multiple discrete random variables from the discrete joint probability distribution

you construct the conditional probability distributions for multiple discrete random variables from the discrete joint probability distribution

you determine whether two discrete random variables are independent from the joint probability distribution

you construct the joint cumulative distribution for multiple discrete random variables from the discrete joint probability distribution

you determine whether two discrete random variables are independent from the joint cumulative distribution

you compute the expected value of a function of multiple discrete random variables from the joint probability distribution

you compute the covariance and correlation of two discrete random variables from the joint probability distribution

you relate the independence of two discrete random variables to their covariance

you compute the expected value and variance of a linear combination of discrete random variables from the joint probability distribution

you relate the variance of a linear combination of discrete random variables to their independence

you verify that a function of multiple continuous random variables is a valid joint probability density function

you construct the marginal or individual probability density functions for multiple continuous random variables by evaluating a multiple integral of the continuous joint probability density function

you construct the conditional probability distributions for multiple continuous random variables from the continuous joint probability density function

you determine whether two continuous random variables are independent from the joint probability density function

you compute the expected value of a function of multiple continuous random variables by evaluating a multiple integral of the continuous joint probability density function

you compute the covariance and correlation of two continuous random variables by evaluating a multiple integral of the continuous joint probability density function

you relate the independence of two continuous random variables to their covariance

you compute the expected value and variance of a linear combination of continuous random variables by evaluating a multiple integral of the continuous joint probability density function

you relate the variance of a linear combination of continuous random variables to their independence

you compute the mean and variance of a sample mean of independent measurements

you compute the mean of a sample variance of independent measurements
Apply Results of Various Sampling Distributions.

Assessment Strategies

in the solution to a problem on a quiz, homework, project or exam

Criteria

you recognize the importance of random sampling from a population

you distinguish random sampling with replacement from random sampling without replacement

you identify the sampling distribution of means

you represent the sampling distribution of means

you distinguish the mean and standard deviation of the parent population from the mean and standard deviation of the sampling distribution of means

you determine the mean of the sampling distribution of means from the mean of the parent population

you calculate the standard deviation of the sampling distribution of means from the mean and standard deviation of the parent population

you recognize the significance of the finite population correction factor in the variance of the sampling distribution of means when the random sampling is done without replacement from a finite population

you verify the content of the Central Limit Theorem by computational simulation

you use the Central Limit Theorem to compute probabilities for a range of values of a sample mean

you calculate at a given level of significance a confidence interval for a sample mean in terms of parent population parameters

you recognize the use of the t distribution to analyze the sampling distribution of means for small random samples taken from a normal distribution with unknown population standard deviation

you identify the correct degrees of freedom associated with a t distribution

you demonstrate the connections between the standard normal distribution and a t distribution

you demonstrate the similarities between the standard normal distribution and a t distribution

you demonstrate the differences between the standard normal distribution and a t distribution

you use a table to locate a critical t score given the degrees of freedom and a probability value, alpha

you identify the sampling distribution of the variance

you recognize the use of the chi-squared distribution to analyze the sampling distribution of the variance for random samples taken from a normal distribution

you identify the correct degrees of freedom associated with a chi-squared distribution

you use a table to locate a critical chi-squared score given the degrees of freedom and a probability value, alpha

you identify the sampling distribution of the of the ratio of two variances taken from two independent samples

you recognize the use of the F distribution to analyze the sampling distribution of the ratio of two variances taken from two independent samples

you identify the correct numerator and denominator degrees of freedom associated with an F distribution

you use a table to locate a critical F score given the numerator degrees of freedom, the denominator degrees of freedom, and a probability value, alpha
Calculate Confidence Intervals for Population Parameters Based on Sample Data.

Assessment Strategies

in the solution to a problem on a quiz, homework, project or exam

Criteria

you distinguish between biased and unbiased estimators of a population parameter

you distinguish between the probability of a future outcome and the level of confidence for an estimate based on data already obtained

you calculate confidence intervals for a population mean in terms of a sample mean and a sample standard deviation for large samples

you demonstrate the connection between the Central Limit Theorem and confidence intervals for the population mean based on large sample sizes

you use the degrees of freedom of the sample variance and the t distribution to calculate confidence intervals for population means when the sample size is small

you state and critically examine the assumptions made in using a t distribution to calculate confidence intervals for population means when the sample size is small

you determine the sample size necessary to attain a prescribed level of precision for a stated level of confidence

you use the sampling distribution of differences of means

you compute the pooled estimate of the variance of two populations of equal variance based on the sample variances

you calculate confidence intervals for the difference of two population means in terms of the sample means and sample standard deviations for both large and small independent samples

you state and critically examine the assumptions made in using a t distribution to calculate confidence intervals for the difference of population means based on small independent samples

you decide when it is appropriate to calculate degrees of freedom based on the Smith-Satterthwaite formula

you distinguish between independent random samples and a matched pair experimental design

you calculate a confidence interval for a difference of two population means using a matched pair experimental design

you use the chi-squared distribution to calculate a confidence interval for a population variance

you state and critically examine the assumptions made in using a chi-squared distribution to calculate confidence intervals for a population variance

you use the confidence interval for a population variance to calculate a confidence interval for the population standard deviation

you calculate confidence intervals for a population proportion in terms of a sample proportion based on a large random sample

you demonstrate the connection between the binomial distribution and a confidence interval for a population proportion

you demonstrate the similarities between confidence intervals for a population mean and a population proportion

you demonstrate the differences between confidence intervals for a population mean and a population proportion

you examine the adequacy of using a normal distribution in generating a confidence interval for a population proportion

you determine the sample size necessary to attain a prescribed level of precision in generating a confidence interval for a population proportion at a stated level of confidence

you calculate confidence intervals for the difference of two population proportions in terms of two independent sample proportions

you demonstrate the similarities between confidence intervals of the differences of two population means and the difference of two population proportions

you demonstrate the differences between confidence intervals of the differences of two population means and the difference of two population proportions

you use technology to compute confidence intervals
Test Hypotheses About Population Parameters Based on Sample Data.

Assessment Strategies

in the solution to a problem on a quiz, homework, project or exam

Criteria

you formulate alternative and null hypotheses from a written statement of a question to be decided

you recognize Type I and Type II errors

you recognize the connection between Type I errors and the level of significance

you distinguish the probability of falsely rejecting the null hypothesis, alpha, from beta, the probability of failing to reject the null hypothesis when the alternative hypothesis is true

you distinguish between one-sided (one tail) and two-sided (two tail) hypotheses tests

you recognize and interpret a operating characteristic curve for one-sided and two-sided alternative hypotheses

you recognize the connection between two-sided tests and confidence intervals

you distinguish the observed sample statistic from the corresponding critical score obtained from a probability distribution

you recognize the appropriate criterion for rejecting the null hypothesis

you formulate the appropriate rejection (critical) region based on the critical score and the alternative hypothesis

you perform one-sided (one tail) and two-sided (two tail) hypotheses tests about a population mean

you perform one-sided (one tail) and two-sided (two tail) hypotheses tests about a population proportion

you perform one-sided (one tail) and two-sided (two tail) hypotheses tests about the difference of two population means based on independent samples

you perform one-sided (one tail) and two-sided (two tail) hypotheses tests about the difference of two population means based on a matched pair experimental design

you perform one-sided (one tail) and two-sided (two tail) hypotheses tests about the difference of two population proportions

you perform one-sided (one tail) and two-sided (two tail) hypotheses tests about a population variance using a chi-squared distribution

you use the chi-squared distribution at a given level of significance to test whether the disagreement between theoretical and empirical probabilities is not random (a "Goodness of Fit" test)

you recognize when empirical and theoretical probability distributions are in agreement based on their graphs

you provide valid justification for the use of a chi-squared distribution in testing whether the disagreement between theoretical and empirical probabilities is not random

you test whether two categorical variables are dependent by performing a contingency table analysis using a chi-squared distribution

you perform one-sided (one tail) and two-sided (two tail) hypotheses tests about two population variances based on two independent samples and the F distribution

you calculate P-values for hypotheses tests using the standard normal distribution

you interpret P-values for hypotheses tests using the standard normal distribution

you estimate P-values for hypotheses tests that use the t, chi-squared or F distributions

you interpret P-values for hypotheses tests that use the t, chi-squared or F distributions

you explain the relationship between the stated level of significance of the test and the calculated or estimated P-values

you recognize the underlying assumptions involved in testing a given hypothesis

you recognize the underlying limitations involved in testing a given hypothesis

you use technology to test hypotheses
Interpret a One Way Analysis of Variance.

Assessment Strategies

in the solution to a problem on a quiz, homework, project or exam

Criteria

you recognize a one-way analysis of variance (ANOVA) to test whether there are differences in performance due to a single factor varied at more than two levels

you state and explain the null hypothesis for a one-way ANOVA

you perform a one-way analysis of variance (ANOVA) to test whether there are differences in performance due to a single factor varied at more than two levels

you interpret the treatment sum of squares and the error sum of squares

you identify the degrees of freedom associated with the single treatment factor

you identify the degrees of freedom associated with error

you relate the null hypothesis to the interpretation of the ratio of the treatment mean square to error mean square

you construct an ANOVA table

you use the F distribution in a one-way ANOVA

you state a conclusion consistent with the one-way ANOVA analysis and the stated level of significance

you recognize the underlying assumptions of a one-way ANOVA

you recognize the underlying limitations of a one-way ANOVA

you examine the sample data to check if there is evidence that the underlying assumptions are not valid

you use technology to perform the one-way analysis of variance
Determine Which Levels of a Single Factor Make a Significant Difference in Performance.

Assessment Strategies

in the solution to a problem on a quiz, homework, project or exam

Criteria

you test for which treatment means are different by performing multiple pair comparison tests

you interpret the value of the level of significance used in the multiple pair comparisons

you explain the value of the level of significance used in the multiple pair comparisons

you explain the connections between the conclusions of the one-way ANOVA test and the multiple pair comparisons
Set Up and Calculate a Linear Regression Fit of Bivariate Data.

Assessment Strategies

in the solution to a problem on a quiz, homework, project or exam

Criteria

you distinguish between a deterministic and a probabilistic model description of the relationship between a pair of variables

you distinguish between a control variable (input) and a response variable (output)

you generate the scatter diagram for a set of paired xy data

you paraphrase the method of least squares and its connection to the linear regression equations

you state the underlying assumptions made in the method of least squares applied to a set of paired xy data

you generate the normal equations and from them derive the equations for the regression slope and intercept

you compute the regression slope and the regression intercept from a set of paired xy data

you plot the regression line for a set of paired xy data on the scatter diagram

you use technology to compute the regression slope and intercept and to plot the regression line
Perform Statistical Inference on a Linear Regression Fit of Bivariate Data.

Assessment Strategies

in the solution to a problem on a quiz, homework, project or exam

Criteria

you recognize and state the underlying assumptions made when performing statistical inference on a linear regression analysis

you critically examine for a given data set whether there is evidence that the underlying assumptions are invalid

you recognize the underlying limitations of a linear regression analysis

you perform statistical inference (calculation of a confidence interval or performance of a hypothesis test) on the population slope and population intercept

you calculate confidence intervals for the mean response of y for a given x value

you interpret confidence intervals for the mean response of y for a given x value

you calculate confidence intervals for a single y measurement (future observed value) for a given x value

you interpret confidence intervals for a single y measurement (future observed value) for a given x value

you recognize and quantify the danger of extrapolating beyond the range of experimentation

you use technology to compute the confidence intervals and to perform the hypothesis testing
Examine the Adequacy of a Linear Regression Fit of Bivariate Data.

Assessment Strategies

in the solution to a problem on a quiz, homework, project or exam

Criteria

you calculate the coefficient of determination and the correlation coefficient for a set of paired xy data

you interpret the coefficient of determination and the correlation coefficient for a set of paired xy data

you demonstrate the connections between the regression slope and the correlation coefficient

you compute the degrees of freedom associated with the error variation and the explained variation

you demonstrate the connections between the explained variation, the error variation, ANOVA and the coefficient of determination

you interpret the results of ANOVA applied to the regression fit

you plot graphs of the residuals

you inspect graphs of the residuals for deterministic deviations from a linear model

(OPTIONAL) you recognize that a linear model refers to linearity in the parameters of the model, not to linearity between the response variable and the control variable

(OPTIONAL) you a use linear model employing a curvilinear dependence of response variable to control variable

(OPTIONAL) you determine the form of the curvilinear model from the pattern of residuals

you use technology to compute the coefficient of determination and to plot the residuals
Correlation Analysis

Assessment Strategies

in the solution to a problem on a quiz, homework, project or exam

Criteria

you calculate the correlation coefficient for a set of paired xy data

you interpret the correlation coefficient for a set of paired xy data

you distinguish the assumptions made in a correlation analysis from those made in a regression analysis

you recognize the symmetry treatment of x and y in the correlation coefficient for a set of paired xy data

you distinguish correlation from causation

you recognize the connection between covariance and correlation

you use the bivariate normal distribution and the Fisher Z transformation to perform statistical inference about the population correlation coefficient

you use technology to to perform statistical inference about the population correlation coefficient