T interval & T test
In practical, we don't know 
, so we substitute the standard error
of 
for its standard
deviation 
. Then the statistic ( 
)
we get has a t distribution with n-1 degrees of freedom.
Mean of population 
can be estimated by t value corresponding
to a specified confidence level C. This t interval is 
, where the t* is the upper
(1-C)/2 critcal value for the (n-1) distritution, n is sample
size.
Exercise 7.18 of BPS ( Page 386, Chapter 7 ) describes a gas chromatography study. A specimen contaning 1 nanogram of a compound gave the following reading as shown in worksheet.
Using the TINTERVAL command,
we can get a 95% confidence interval for the mean response to
1 nanogram of this substance.
MTB> tint 95 'specimen reading'
Same result can be obtained by selecting
Stat->Basic Statistics->1-Sample t from menu and
fill out the dialog box as shown. The dialog box for 1-Sample
t is similar to the dialog for 1-Sample Z, except that
it is not necesary to enter a value for Sigma. The dialog
box includs a button for Graphs, which is used to check
the data graphically for outliers or skewness which might threaten
the validity of the t procedures.
The result apears in session window is shown below.
In Exercise 7.18, we want to test that whether the mean is equal or larger than 23.0 ( H0: u = 23.0 Ha: u>23.0). Select Stat->Basic Statistics->1-Sample t from menu and fill out the dialog box as shown. Make sure to specify the alternative hypothesis " greater than" in Alternative box in dialog, because in Minitab two-sided test is defaulted.
The test result is shown below. We find that the P-value is reported as 0.77, so we should hold the noll hypothesis U=23.0.
