# ENGI 4421 - Third Minitab Tutorial Normal Probability Plot & Confidence Interval Simulations using MINITAB

In this session we shall use Minitab® to

# Creation of a Data Set

 We shall simulate the creation of a normal probability plot for a case where the data are known to be non-normal, namely data drawn from an exponential distribution.   The standard exponential distribution (λ = 1) is shown here: Start Minitab. Click on the menu item "`Calc`" Move to "`Random Data`" On the new pop-up menu, click on "`Exponential...`"

 In the new dialog box, Enter ` 100 ` for the number of rows, Type ` C1 ` for the location, Enter ` 1000 ` for the Scale, Leave the Threshold at 0 and Click on the "`OK`" button.

 Type a new name for column ` C1 `. As lifetimes are often random quantities that follow an exponential distribution, we shall use the name ` Lifetime ` here. The column ` Lifetime ` now contains 100 values. Note that, as this is a set of random data, the numbers in your data column will not be identical to those shown here.

# Graphical Summary of the Data

 As we have done before, we can use Minitab to gain a first impression of the distribution of our newly-generated data. Click on the menu item "`Stat`", Move to "`Basic Statistics`" and Click on "```Display Descriptive Statistics...```".

 In the dialog box, Double click on "`C1 Lifetime`" to select it into the "`Variables`" pane, then Click on the "`Graphs...`" button.

 In the new dialog box, Check the boxes "```Histogram of data, with normal curve```" and "`Boxplot of data`" and Click on the "`OK`" button. Back in the "```Display Descriptive Statistics```" window, click on the "`OK`" button.

Two graph windows then appear:

The evidence for positive skew is overwhelming.
The histogram shows a long right tail and no left tail.

The boxplot shows the upper quartile to be further away from the median than the lower quartile.
The boxplot’s upper whisker is much longer than its lower whisker.
There are several outliers, all on the positive side.
From the Session window,

The mean is much greater than the median.

[Note also that the values of sample mean and sample standard deviation are consistent with equality of the population mean and population standard deviation, which is true of any exponential distribution.]

Clearly the normal distribution does not fit these data.

# Confidence Intervals

We shall use Minitab to

• simulate drawing a random sample from a known normal population,
• construct one- and two-sided confidence intervals for the mean,
• draw inferences on the true value of the mean from the confidence intervals.

Also available here is a Minitab macro to simulate the construction of confidence intervals, from many random samples, 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%.