Supplementary Exercise 6.108 of IPS7e
-------------------------------------

Brief solution only.
Minitab commands and output:

MTB > OneZ 100 483;
SUBC>   Sigma 100;
SUBC>   Test 480;
SUBC>   Confidence 95.0;
SUBC>   Alternative 1.
One-Sample Z 

Test of mu = 480 vs > 480
The assumed standard deviation = 100

  N   Mean  SE Mean  95% Lower Bound     Z      P
100  483.0     10.0            466.6  0.30  0.382

MTB > OneZ 1000 483;
SUBC>   Sigma 100;
SUBC>   Test 480;
SUBC>   Confidence 95.0;
SUBC>   Alternative 1.
One-Sample Z 

Test of mu = 480 vs > 480
The assumed standard deviation = 100

   N    Mean  SE Mean  95% Lower Bound     Z      P
1000  483.00     3.16           477.80  0.95  0.171

MTB > OneZ 10000 483;
SUBC>   Sigma 100;
SUBC>   Test 480;
SUBC>   Confidence 95.0;
SUBC>   Alternative 1.
One-Sample Z 

Test of mu = 480 vs > 480
The assumed standard deviation = 100

    N    Mean  SE Mean  95% Lower Bound     Z      P
10000  483.00     1.00           481.36  3.00  0.001


Comments:
---------
In the first two scenarios, the z-statistic is non-significant, 
but in the third scenario it becomes strongly significant. The 
z-statistics go up with a factor of sqrt(10)=3.16 for every factor
10 increase in the sample size.