Example 11.05 provides the following information
An investigator wants to know which of two electric toasters has the greater ability to resist the abnormally high electrical currents that occur during an unprotected power surge. Random samples of six toasters from factory A and five toasters from factory B were subjected to a destructive test, in which each toaster was subjected to increasing currents until it failed. The distribution of currents at failure (measured in amperes) is known to be approximately normal for both products, with a common (but unknown) population variance. The results are as follows:
Factory A: 20 28 24 26 23 26
Factory B: 21 18 19 17 22
Conduct the appropriate hypothesis test.
Start a new project in Minitab. Enter the data into the worksheet. [In order to rename a worksheet, |
 |
 |
In the main menu, then place the cursor on
" then click on the menu item
" |
Click on the radio button
"Samples in different columns",
Click anywhere in the box "First:",
(so that the column names appear in the left pane),
Select column "C1 A" into the
box "First:",
Select column "C2 B" into the
box "Second:",
Check the box "Assume equal variances"
and click on the "Options..." button.
 |
Change the confidence level Click on the " |
In the Session window, the following results appear:
For any of the following reasons, we can reject the null hypothesis
at a level of significance of 1%:
(difference = 0) is not in the confidence interval; or
the t value of 3.36 is greater than the critical value
t.005, 8 = 3.25; or
the P-value, .008, is less than 1% (though not by much!).
One may also examine the custom
Excel spreadsheet
demos/t2Unpaired.xls:
Example 11.06 provides the following example for a paired t-test.
Nine volunteers are tested before and after a training programme. Based on the data below, can you conclude that the programme has improved test scores?
Volunteer: 1 2 3 4 5 6 7 8 9 After training: 75 66 69 45 54 85 58 91 62 Before training: 72 65 64 39 51 85 52 92 58
Start a new project in Minitab.
Enter the data into the worksheet.
[Click here to skip the topic of transposing rows
and columns in a Minitab worksheet.]
If we use a copy and paste from this web page,
then the data appear in rows instead of columns.
Having copied the two rows of data from the web page into the clipboard, click on the first white cell in the data window and paste at that location.
In the resulting pop-up box, accept the default,
"Use spaces as delimiters",
so that the worksheet appears similar to this.
 |
To correct this problem, proceed as follows. In the main menu, then click on the menu item
" |
Enter "C3-C11" into the top right pane.
Select the radio button "After last column in
use".
Click on the "OK" button.
 |
The data appear in the final columns. Select the header of the first column
" |
Right click on this selection and click on
" |
 |
 |
The desired data are now in columns 1 and 2. Click in the header space just above the first cell and give appropriate names to these columns |
To rename the worksheet,
retrieve the Project Manager. Right-click on the name "Worksheet 1", |
 |
 |
The worksheet is now ready. |
 |
In the main menu, then place the cursor on
" then click on the menu item
" |
In the dialog box, Click anywhere in the box Select column " Select column " and click on the |
 |
 |
Change the confidence level click on the down-arrow Click on the " |
In the Session window, the following results appear:
For any of the following reasons, we can reject the null hypothesis
at a level of significance of 1%:
(difference = 0) is below the bottom of the confidence interval; or
the t value of 3.53 is greater than the critical value
t.010, 8 = 2.90; or
the P-value, .004, is less than 1%.
One may also examine the custom
Excel spreadsheet
demos/t2test.xls:
Example 12.02 (Simple Linear Regression) is based on the identical data set to the paired t-test example above.
We can find the equation of the line of best fit through the data in the least squares sense, as follows.
With the worksheet containing in the main menu, then place the cursor on
" then click on the menu item |
 |
Click anywhere in the box
"Response [Y]:",
(so that the column names appear in the left pane),
Select column "C1 After" into the box
"Response [Y]:",
Select column "C2 Before" into the box
"Predictor [X]:",
and click on the "Graphs..." button.
 |
Click on the radio button "Four in one". click on the "OK" button. |
Back in the "Fitted
Line Plot" main dialog box,
click on the "Options..." button.
Check the box "Display confidence interval".
Supply an appropriate title.
Click on the "OK" button.
The following graphs are produced.
With a coefficient of determination above 99%, it is no surprise that all of the nine points lie very close to the same straight line.
The ANOVA table and other information appear in the Session window.
The method of simple linear regression requires the
assumption that the residuals are independent and identically
distributed, with a normal distribution of zero mean and
constant variance. Due to the options exercised in the
"Graphs..." dialog box, we can check
this assumption.
 |
Among the four graphs in the "Residual Plots for After" graph window is this normal probability plot of the residuals. We can see that the residuals do appear to be consistent with the assumption of normality. |
[Return to the index of
demonstration files]
[Return to your previous page]
