Supplementary Exercise 6.95 of IPS7e
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Measurements of radon concentrations by radon detectors placed in a test
chamber. The true concentration is known to be 105 pCi/l, so the purpose 
of the experiment is to test the accuracy of the detectors.

Let X_1,...,X_12 denote the 12 measurements.
We assume that the observations are i.i.d. (independent and identically
distributed) with mean mu and standard deviation sigma.
We also assume (unrealistically) that sigma is known to be 9.
The average of X's (Xmean) 104.133.

(a) 95% confidence interval for the mean reading in the chamber:
Xmean +- 1.96*sigma/sqrt(n) = 104.133 +- 1.96*9/sqrt(12) 
                            = 104.133 +- 5.092 = (99.0 , 109.2)

(b) Hypothesis H0: mu=105, alternative hypothesis Ha: mu <> 105.
The z-statistic for H0 against Ha is significant at the 5% level, if
a 95% two-sided confidence interval for mu DOES NOT include 105.

The interval from (a) however easily includes 105, so there is no
significant evidence against the true value being 105. As shown by the
Minitab output below, the P-value is 0.74.

Note that the population studied consists of detectors of the given
type placed in the same chamber (possibly extendable to another 
environment with the same radon concentration).

As a final remark, the 12 observations do seem to correspond reasonably well
to a normal distribution, despite some right-skewness (as evaluated by stem plot,
probability plot and normality test), so that there is no need to worry about
the normality of Xmean.

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Minitab commands and output:

MTB > WOpen "H:\VHM\VHM801\Datasets\Minitab\Chapter 6\ex06_095.mtw".
Retrieving worksheet from file: 'H:\VHM\VHM801\Datasets\Minitab\Chapter
6\ex06_095.mtw'
Worksheet was saved on 02/10/2014

MTB > Describe 'radon';
SUBC>   Mean;
SUBC>   SEMean;
SUBC>   StDeviation;
SUBC>   QOne;
SUBC>   Median;
SUBC>   QThree;
SUBC>   Minimum;
SUBC>   Maximum;
SUBC>   Skewness;
SUBC>   Kurtosis;
SUBC>   N;
SUBC>   NMissing.
Descriptive Statistics: radon 

Variable   N  N*    Mean  SE Mean  StDev  Minimum     Q1  Median      Q3
radon     12   0  104.13     2.71   9.40    91.90  96.90  102.75  109.90

Variable  Maximum  Skewness  Kurtosis
radon      122.30      0.85     -0.01

MTB > Stem-and-Leaf 'radon';
SUBC>   Trim.
Stem-and-Leaf Display: radon 

Stem-and-leaf of radon  N  = 12
Leaf Unit = 1.0

 1   9   1
 5   9   5679
(3)  10  134
 4   10  5
 3   11  1
 2   11  9
 1   12  2

MTB > PPlot 'radon';
SUBC>   Normal;
SUBC>   Symbol;
SUBC>   FitD;
SUBC>   Grid 2;
SUBC>   Grid 1;
SUBC>   MGrid 1.
Probability Plot of radon 
The P-value for the Anderson-Darling test is 0.311.

MTB > OneZ 'radon';
SUBC>   Sigma 9;
SUBC>   Test 105;
SUBC>   Confidence 95.0;
SUBC>   Alternative 0.
One-Sample Z: radon 

Test of mu = 105 vs not = 105
The assumed standard deviation = 9

Variable   N    Mean  StDev  SE Mean       95% CI          Z      P
radon     12  104.13   9.40     2.60  (99.04, 109.23)  -0.33  0.739