Supplementary Exercise 6.140 of IPS7e
-------------------------------------

Dimethyl sulfide (DMS) thresholds for 10 beginning students of oenology.

Data: X1,...,X10.

Model: X1,...,X10 are i.i.d. (a SRS) and normally distributed
N(mu,sigma), where mu is unknown and sigma=7 mug/l.


(a) Minitab commands and output:

MTB > WOpen "H:\VHM\VHM801\Datasets\Minitab\Chapter 6\ex06_140.mtw".
Retrieving worksheet from file: 'H:\VHM\VHM801\Datasets\Minitab\Chapter
6\ex06_140.mtw'
Worksheet was saved on 02/10/2014

MTB > Describe 'odor'.
Descriptive Statistics: odor 

Variable   N  N*   Mean  SE Mean  StDev  Minimum     Q1  Median     Q3  Maximum
odor      10   0  30.60     1.92   6.08    20.00  24.75   31.50  35.25    40.00

MTB > Stem-and-Leaf 'odor'.
Stem-and-Leaf Display: odor 

Stem-and-leaf of odor  N  = 10
Leaf Unit = 1.0

 2   2  04
 3   2  5
(4)  3  0123
 3   3  56
 1   4  0

Comment:
The distribution looks indeed roughly symmetric with no outliers, 
although it is difficult to assess distribution shape from such a small 
sample.

MTB > PPlot 'odor';
SUBC>   Normal;
SUBC>   Symbol;
SUBC>   FitD;
SUBC>   Grid 2;
SUBC>   Grid 1;
SUBC>   MGrid 1.
Probability Plot of odor 

Comment:
The points in the normal probability plot are close to the straight line,
and the P-value of the Anderson-Darling normality test is 0.82.
There is no evidence against a normal distribution of the data.


(b) The Minitab listing gives a 95% confidence interval for the mean DMS odor
threshold:

MTB > OneZ 'odor';
SUBC>   Sigma 7;
SUBC>   Confidence 95.0;
SUBC>   Alternative 0.
One-Sample Z: odor 

The assumed standard deviation = 7

Variable   N   Mean  StDev  SE Mean      95% CI
odor      10  30.60   6.08     2.21  (26.26, 34.94)


(c) We set up the hypotheses:
  
  H0: mu = 25mug/l, versus Ha: mu > 25mug/l

We choose a one-sided alternative hypothesis because interest is only in a
higher threshold for the untrained students. Also here, a two-sided 
alternative hypothesis could be justified as well.

The Minitab listing gives a z-test.

MTB > OneZ 'odor';
SUBC>   Sigma 7;
SUBC>   Test 25;
SUBC>   Confidence 95.0;
SUBC>   Alternative 1.
One-Sample Z: odor 

Test of mu = 25 vs > 25
The assumed standard deviation = 7

Variable   N   Mean  StDev  SE Mean  95% Lower Bound     Z      P
odor      10  30.60   6.08     2.21            26.96  2.53  0.006

Comments:
---------
The P-value is 0.006, so we reject H0 and conclude that the students indeed
have a higher DMS odor threshold.

Technical note: when we use a one-sided alternative for the test, the
listing also displays a one-sided confidence interval (CI). In the course,
one-sided CIs are not discussed, and it is therefore recommended to simply 
ignore the information about CIs when a one-sided alternative is used.
If both a CI and a test are desired, one will need to use the menu
twice.