Index of Demonstration Files

• Minitab sessions
• QuickBASIC programs
• Excel Spreadsheets
• Histogram Creation in Excel or Minitab
• Miscellaneous

Minitab Tutorial Sessions

The following web pages duplicate the tutorial sessions in which the Minitab^® software will be used.

•   Session 1:   Descriptive Statistics 1 (100 observations of shear strengths:
                      retrieve file, sort data, stem-and-leaf diagram, bar chart, histogram)
•   Session 2:   Descriptive Statistics 2 (100 observations of shear strengths:
                      summary statistics, boxplot & graphs)
•   Session 3:   Descriptive Statistics 3 (Model of lamp lifetimes:   summary statistics & graphs)
•   Session 4:   Empirical Probability 1 (Coin Tossing Example);
  (includes a separate page to generate the macro code for a time series plot from the graphical interface)
•   Session 5:   Empirical Probability 2 (Shared Birthdays Example)
•   Session 6:   Normal Probability Plots
•   Session 7:   Inferences on Two Samples and Simple Linear Regression

Also available is a condensed list of instructions on how to use Excel or Minitab to create an histogram or a normal probability plot.

An extension to Bayes’ theorem:
This text provides a formula for finding the posterior probability of an event A_i after a pair of exchangeable (identical and independent) tests have produced results B_j and C_k.
Also available is an associated Excel file.

Excel Spreadsheet Files

Some browsers will run the Excel program automatically upon clicking on a .xls file.   Otherwise, you will have to save the file and open it from inside Excel.

The two most important files are tables of values, a paper copy of which will be provided to you when it is required in a test or the final examination.   These tables are also provided as Chapter 15 of the Lecture Notes.

• t Tables:
  This Excel spreadsheet file contains a table of some critical values   t _{a, n}   of the t distribution.

• Standard Normal c.d.f. (z Tables):
  This Excel spreadsheet file contains a table of values for the standard normal cumulative distribution function, F(z).

The other Excel files are presented in the order of the chapters in which they appear in the lecture notes.

Chapter 3:   Elementary Probability

• VennIn:
  Completes a 3-event Venn diagram from information on the probabilities of unions of events
• VennOut:
  Completes a 3-event Venn diagram from information on the probabilities of intersections of events

Chapter 4:   Counting Techniques

• Counts:
  Comparison of numbers of selections, according to whether selection is with/without replacement and ordered/unordered

Chapter 5:   Independence; Bayes’ Theorem

• Bayes Tree Diagram:
  Calculates conditional probabilities using a simple tree diagram version of Bayes’s theorem; (only two branches at each of only two nodes).

• bayes6:
  Posterior distribution of p, given 4 successes in 6 trials and no prior knowledge of p
• bayes3:
  Posterior distribution of p, given 2 successes in 3 trials and no prior knowledge of p
• bayepair:
  Illustration of bayesext.html; chain of Bayes results
• birthday:
  Explores the classic “Birthday problem”.   Only 23 randomly chosen people need to be in a room in order for it to be odds on that at least two of them share the same birthday.

Chapter 6:   Discrete Random Quantities

• Discrete Probability Distribution:
  You can enter values of x and p(x) for an arbitrary probability mass function (up to eleven possible values of X) into this Excel spreadsheet file.   The cumulative distribution function, expected value, variance and standard deviation are all displayed, together with some intermediate calculations.

• Probability Distribution for Runs of Wins:
  The probability distribution for   R , the number of runs of consecutive wins in a randomly arranged sequence of n wins and m losses, is displayed as both a table and a graph.
  You can choose the values of n and m.

Chapter 7:   Discrete Probability Distributions

• Binomial Probability Distribution:
  This Excel spreadsheet file displays the value of the expected value E[X] and variance V[X] for a particular binomial probability distribution.   It also displays the values of both the probability mass function (p.m.f.) and the cumulative distribution function (c.d.f.) at your chosen value of x (with your chosen values for the parameters n and p), for the binomial probability distribution and for the Poisson and Normal approximations (even when not appropriate!).   An extract of associated tables of values and graphs of both the p.m.f. and the c.d.f. for the binomial probability distribution (for your chosen values of n and p and for various values of x) is also displayed.

  A paper copy of an appropriate version of this table will be provided to you when it is required in a test or the final examination.

• Hypergeometric Probability Distribution:
  This Excel spreadsheet file displays the value of the expected value E[X] and variance V[X] for a particular hypergeometric probability distribution.   It also displays the values of both the probability mass function (p.m.f.) and the cumulative distribution function (c.d.f.) at your chosen value of x for your chosen values of the parameters N (population size), n (sample size) and M (number of successes in the population), for the hypergeometric probability distribution and for the corresponding binomial probability distribution.   An extract of associated tables of values and graphs of both the p.m.f. and the c.d.f. for the hypergeometric probability distribution (for your chosen values of N, n and M and for various values of x) is also displayed.

• Poisson Probability Distribution:
  This Excel spreadsheet file displays the value of the variance V[X] for a particular Poisson probability distribution.   It also displays the values of both the p.m.f. and the c.d.f. at your chosen value of x (with your chosen value for the parameter µ = E[X]), for the Poisson probability distribution and for the Normal approximation (even when it is not appropriate!).   An extract of associated tables of values and graphs of both the p.m.f. and the c.d.f. for the Poisson probability distribution (for your chosen value of µ   and for various values of x) is also displayed.

  A paper copy of an appropriate version of this table will be provided to you when it is required in a test or the final examination.

• Negative Binomial Probability Distribution:
  This Excel spreadsheet file displays the value of the expected value E[X] and variance V[X] for a particular negative binomial probability distribution, (where x = the number of trials when the n^th success occurs — note that the Devore textbook adopts a different definition for the random quantity X).

  It also allows you to follow the evolution of the graph of the p.m.f. as you change the values of the two parameters.

• Geometric Probability Distribution:
  

  Tabulates and displays the graphs of both the p.m.f. and the c.d.f. for the Geometric probability distribution for user-chosen values of the parameter.

Chapter 8:   Continuous Probability Distributions

• z value Calculator:
  Finds c.d.f. values and   P[a < X < b] when X ~ N(µ  , s ²), for user-chosen mean and standard deviation.

  It also finds   F(z) = P[Z < z]   for any   z   or you may find the value of   z   that generates a particular value of a in the equation   P[|Z| > z]   =   a .

• t value Calculator:
  In this very small spreadsheet file, you may find   P[T > t]   for any   t   and for any number of degrees of freedom, or you may find the value of   t   that generates a particular value of a in the equation   P[T > t]   =   a .

• Gamma Probability Distribution:
  Displays the value of the expected value E[X], mode, median, variance V[X] and P[a < X < b] for a particular gamma probability distribution with user-chosen values of a, b and the parameters a and b.   It also displays graphs of both the probability density function (p.d.f.) and the cumulative distribution function (c.d.f.) for both the gamma distribution and that normal distribution with the same values of mean and variance.

• Beta Probability Distribution:
  This file displays the graphs of the p.d.f. and c.d.f. of the Beta distribution, for user-chosen parameter values.

• Weibull Probability Distribution:
  This file displays the graphs of the p.d.f. and c.d.f. of the Weibull distribution, for user-chosen parameter values.

• F Probability Distribution Graph:
  This file displays the graph of the p.d.f. of the F distribution, for user-chosen numbers of degrees of freedom.

  F Probability Distribution Calculator:
  Evaluates P[F > f] for the F distribution, for any chosen numbers n₁ and n₂ of degrees of freedom at any chosen value of f.
  Also evaluates the critical value of f, to the right of which a of the probability lies.
  Other tabs display the critical values of the F distribution at 5% and 1% levels of significance (the traditional tables of the F distribution).

Chapter 9:   Joint Probability Distributions

• Joint p.m.f.:
  Displays a [discrete] joint probability mass function and evaluates the correlation coefficient.
  (Initial data are from Example 09.01)

• Central Limit Theorem:
  Displays the probability density graphs of the sample mean for a Bernoulli random quantity for sample size n = 1, 4, 16 and 64.   The Central Limit Theorem approach to normality can be seen.

Chapter 10:   Interval Estimation (One Sample)

• Bayes Confidence Interval for µ :
  Bayesian confidence interval / hypothesis test on the mean, from summary statistics
  (Initial data are from Example 10.07)

• Bayes Confidence Interval for µ :
  Bayesian confidence interval / hypothesis test on the mean, from raw data

• Classical & Bayes Confidence Intervals for p :
  Classical and Bayesian confidence intervals on the population proportion p, from the observation of x successes in n trials.

• Bayes Confidence Interval for p :
  Tool to find a precise Bayesian confidence interval for the population proportion p, from no prior opinion and from the observation of x successes in n trials.

Chapter 11:   Hypothesis Tests (One and Two Samples)

• Classical One Sample t-test (from summary statistics):
  Displays the calculations for classical confidence intervals and one sample t tests for the population mean   µ, starting with sample mean and standard deviation.
  (Initial data are from Example 11.01)

• Classical One Sample t-test (from raw data):
  Displays the calculations for classical confidence intervals and one sample t tests for the population mean   µ from the raw data.

• Classical One Sample t-test for Proportions:
  Displays the calculations for a one sample test/CI on a population proportion.
  (Initial data are from Example 11.03)

• Power of Classical One Sample t-test for Proportions:
  Tabulates the power of a one sample test/CI on a population proportion, as a function of the true value of p (or, in the second tab, as a function of the sample size n).

• Power of Classical One Sample t-test for Proportions:
  Finds the minimum sample size needed, to distinguish p₁ from p₀ at desired error levels a and b

• Two Sample t-test:
  Displays the calculations for the unpaired two sample t test for the difference of two means (different sample sizes).
  (Initial data are from Example 11.05)

• Two Sample t-test:
  Displays the calculations for both paired and unpaired two sample t tests for the difference of two means (equal sample sizes).
  (Initial data are from Example 11.06)

• Two Sample t-test for Proportions:
  Displays the calculations for a two sample test/CI on the difference in two population proportions.
  (Initial data are from Example 11.07)

Chapter 12:   Simple Linear Regression

• Simple Linear Regression (2):
  Excel spreadsheet file for Example 12.02 of Simple Linear Regression.

• Simple Linear Regression (3):
  Excel spreadsheet file for Example 12.03 of Simple Linear Regression (including confidence and prediction intervals).

• Coefficient of Determination (Simple Linear Regression):
  Table of minimum sample coefficient of determination r ² needed for statistical significance as a function of sample size n, when the null hypothesis is zero population correlation

QuickBASIC Programs

In order to use the QuickBASIC programs below,
either
        click on the file name to run it immediately,
or
        click on the "Source Code" link and save the file to a drive or diskette,
        then run QuickBASIC or QBASIC and open the file from inside that program.

• cointoss.exe : QBASIC program: Evolution of Relative Frequency (# heads in n tosses of a fair coin, as n increases; equivalent to Minitab session 4 above)
  (Source Code)
   
  
• birthday.exe : QBASIC program: Simulation for P[at least 2 people in a room of 25 share a birthday] (equivalent to Minitab session 5 above)
  (Source Code)
   
  
• clt.exe : QBASIC program for the Central Limit Theorem (sample average of n die rolls)
  (Source Code)
   
  
• ci.exe : QBASIC program to simulate confidence intervals for a population mean
  (Source Code)

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