The Minitab® software package is installed on the
computers in rooms EN 3000 / 3029.
Students should be able to download and install Minitab on a home Windows
computer from a link at my.mun.ca,
as mentioned on the MUN ITS
web site.
Note that the Mac version of Minitab lacks many important features of
the Windows version. You will need the Windows version to
complete the assignments.
ENGI 4421 assumes that you have Minitab version 21 (for Windows) installed. However, for future reference, approximate equivalents for the tutorials in Microsoft Excel® are also provided here.
Some browsers will run the Excel program automatically upon clicking
on a .xlsx file. Otherwise, you will have to save
the file and open it from inside Excel.
The three most important files are tables of values, a 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 17 of the Lecture Notes.
t Tables:
A table of some critical values t
a, n
of the t distribution.
Standard Normal c.d.f. (z
Tables):
A table of values for the standard normal cumulative distribution
function,
Chi-Square Tables:
A table of some critical values c2
a, n
of the c 2 distribution.
The other Excel files are presented in the order of the chapters in which they appear in the lecture notes.
Chapter 2: Elementary Probability
Cointoss:Chapter 3: Counting Techniques
Counts:Chapter 4: Laws of Probability; Bayes’ Theorem
VennIn:VennOut:Indep3way: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:bayes3:bayepair:birthday:Chapter 5: 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: Joint Probability Distributions
Joint p.m.f.:
Enter a [discrete] joint probability mass function.
The covariance and correlation coefficient are calculated.
(Initial data are from Example 7.01)
Chapter 8: Propagation of Error
Weighted Mean:
From two independent estimates for m
of unequal uncertainty,
calculates the overall estimate with minimum uncertainty.
(Initial data are from Example 8.04)
Chapter 9: Discrete Probability Distributions
The following spreadsheet files display values of the pmf (probability mass function) and the cdf (cumulative distribution function for some values of the discrete random quantity X, together with the expected value E[X] and variance V[X], for user-chosen values of the parameter(s).
A paper copy of an appropriate version of the Binomial or Poisson table will be provided to you if it is required in a test or the final examination.
Chapter 10: Continuous Probability Distributions
Exponential and Poisson Probability
Distributions:
For a chosen mean time µ to the next event,
evaluates
P[t1 < T < t2]
and evaluates P[N < n]
for the associated Poisson random quantity
N = number of events occuring in a time interval
t (chosen by the user).
z value
Calculator:
Finds c.d.f. values and
P[a < X < b] when
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
t value Calculator:
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
c2
value Calculator:
You may find
P[c2 > c] for any
c
and for any number of degrees of freedom,
or you may find
the value of c that generates a particular
value of a
in the equation
Gamma Probability Distribution:
Displays the value of 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.
Variation: User supplies mean
and standard deviation; the spreadsheet calculates the
parameters a
and b, together with
the other features noted above.
Beta Probability
Distribution:
Displays the graphs of the p.d.f. and c.d.f. of the Beta
distribution, for user-chosen parameter values.
Variation: User supplies mean
and standard deviation; the spreadsheet calculates the
parameters a
and b, together with
the other features noted above. Also available are the details of this calculation.
Weibull Probability
Distribution:
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:
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
n 1
and
n 2
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 11: Interval Estimation (One Sample)
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.
The user selects the probability p of success
in each Bernoulli trial.
Confidence Interval
for µ :
simulates drawing 100 random samples each of size n from a
normal population of known population standard deviation
s and determining what proportion of the 95%
confidence intervals capture the true value of the population
mean m.
A Minitab simulation of confidence intervals is
also available.
Bayes Confidence Interval
for µ :
Bayesian confidence interval / hypothesis test on the mean,
from summary statistics
(Initial data are from Example 11.07)
Confidence Interval
for p :
Classical confidence interval / hypothesis test on the population
proportion, including the Agresti-Coull modification
(Initial data are from Problem Set 8 Question 1)
Chapter 12: Interval Estimation (Two Samples)
Confidence Interval
for p 1 –
p 2 :
Confidence interval on the difference in population proportions
(Initial data are from Example 12.02)
Confidence Interval
for µ 1 –
µ 2 :
Confidence interval on the difference in means, small samples,
from raw data (up to 12 values in each sample)
(Initial data are from Example 12.04)
Chapter 13: Hypothesis Tests
Classical One Sample t-test
(from summary statistics):
Displays the calculations for classical confidence interval
and one sample t test
for the population mean µ, starting with
sample size, sample mean and standard deviation.
(Initial data are from Example 13.02)
Classical One Sample t-test
(from raw data):
Displays the calculations for classical confidence interval
and one sample t test
for the population mean µ from the raw
data (up to a maximum of 100 values).
Type 2 Error Probability
for classical hypothesis tests on µ.
(Initial data are from Problem Set 9 Question 7)
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 latter tabs, 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
(from summary statistics):
Starting with summary statistics (mean, standard deviation and sample size)
shows results of an unpaired two sample t test
for the difference of two means (equal sample sizes) for any
sample sizes.
(Initial data are from Example 13.03)
Two Sample t-test
(from raw data):
Starting with raw data (up to 12 values in each sample), 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 13.05)
Chapter 14: Chi-Square Distribution
Chi-Square Goodness of Fit
Test:
Example 14.01 (loaded die; uniform model) for the
c 2 goodness-of-fit test.
Chi-Square Test for
Independence:
Example 14.02 (independence of lengths and diameters) of the
c 2 independence test.
Chapter 15: Simple Linear Regression
Example 15.02 (from data) –
sample sizes up to 16
Example 15.02 (from the six
summary statistics)
Example 15.02 (Minitab project, for the
normal probability plot)
Example 15.03 (from data) –
sample sizes up to 16 – also includes confidence and prediction
intervals
Example 15.03 (from the six
summary statistics)
Also available is a condensed list of instructions on how to use
Excel to create an histogram or
a normal probability plot.
bDaysProb.html :
HTML/Java demonstration for the evaluation of an empirical probability
for at least 2 of n randomly chosen people sharing a
birthday.CLT.html :
HTML/Java demonstration for the Central Limit Theorem
(sample average of n die rolls)CI_simulation.pdf :
Instructions for a Minitab macro
CI.mac to simulate confidence
intervals for a population mean and to show that the proportion
of 95% confidence intervals that capture the true value of the
population mean is close to 95%.CI_simulation.mpx
An extension to Bayes’ theorem:
This text provides a formula for finding the posterior probability
of an event Ai after a pair of exchangeable
(identical and independent) tests have produced results
Bj and Ck.
Also available is an associated Excel
file.
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