Question

1.   For Each of the following series of measurements values, determine whether any measurements should be rejected at the 90 percent confidence level. After rejecting values where appropriate, determine S, Sm, and ? (95 percent confidence limit) for each series.
a.   2.8    2.7   2.7   2.5   2.9   2.6   3.0   2.6
b.   9713 97.10   97.20   97.35   97.10   97.19  
c   0.134   0.120   0.109   0.124   0.131   0.119   0.135   0.132   0.132

Answer 1

Serie a

All values are accepted

S= 2.73

Sm=0.17

t (n-1)= t(8-1)= t(7)= 2.365

N= measurements values

Series b

S= 97.18; Sm= 0.09

t (0.1, n=5)=2.015

Therefore is necessary rejected the value 97.35

S=97.14

Sm=0.05

t(0.1, n=5) =2.132

C.L= 97.10-97.18-----.> 97.20 and 97.20 are out of the interval of confidence (90%)

The serie b is: 97.10, 97.10, 97.13

S=97.11

Sm=0.02

Confidence interval to 95 %

t_{(0.05, n=2)}=4.303

L.C=97.07-97.15

Serie C

The values: 0.109, 0.119, 0.120 and 0.124 are rejected at 90 % confidence level

the Serie C is: 0.131, 0.132, 0.132, 0.134, 0.135

S= 0.133

Sm= 0.002

t_{(0.05, n=4)}=2.776