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A measurement x1, with
and
I am making a second measurement x2
of the same analyte.
Random!
It has the same We do not know it!
It has the same
As an estimate of my unknown I will use average
221 xx
x
22 222
2121
22
2
221
av
Case 3: We know:
Standard deviation Real value ?
Take N measurements; calculate average as
N
xxxx N
...21
Nx
2 with 95% probability
Coinfidence interval (CI)
Case 4 We know nothing: Mean - ? Standard deviation -?Take N measurements; calculate average as
N
xxxx N
...21
Calculate standard deviation as
1
)(...)()( 222
21
N
xxxxxxs N
Confidence interval?
I do not know
Case 4 We know nothing: Mean - ? Standard deviation -?Take N measurements; calculate average as
N
xxxx N
...21
Calculate standard deviation as
1
)(...)()( 222
21
N
xxxxxxs N
N
stx 95 with 95% probability
Coinfidence interval (CI)
I titrate an unknown solution using a class A50 mL burette. My results show standard deviationof 0.05 mL. How many mesurements I need in order to get confidence interval of ±0.01 mL?
44.02
05.07.12
N=2
08.04
05.018.3
N=4
038.09
05.03.2
N=9
02.020
05.01.2
N=20
009.0120
05.098.1
N=120
Ubur = 0.05 mL
22randomburtotal uuu
44.005.044.0 22 totalu
095.005.008.0 22 totalu
06.005.0038.0 22 totalu
054.005.002.0 22 totalu
05.005.0009.0 22 totalu