Question

the concentration of the cyanobacteria toxin ß-n-methylamino-l-alanine (bmaa) was measured in ground water and found to be 9.27 ppm , 9.88 ppm, 10.30 ppm, and 10.32 ppm. calculate the absolute 95 % confidence interval. round your absolute 95% cl at the first uncertain digit.

Answer 1

Mean=M=sum of all observations/total no of observations=9.27+9.88+10.30+10.32/4=9.94

calculate standard deviation=S=[∑(X-M)^2/N]^1/2

X-M calculations

9.27-9.94=-0.67

9.88-9.94=-0.06

10.30-9.94=0.36

10.32-9.94=0.38

Squarring these numbers,( X-M)^2

(-0.67)^2=0.45

(-0.06)^2=0.0036

(0.36)^2=0.13

(0.38)^2=0.14

S=[∑(X-M)^2/N]^1/2=[0.45+0.0036+0.13+0.14/4^1/2=(0.18)^1/2=0.425

Standard error of true population=SE=S/(N)^1/2=0.425/(4)^1/2=0.425/2=0.212

Calculations of 95% CI=Mean+/- 1.96*SE

=9.94+1.96*0.212=10.35

And 9.94-1.96*0.212=9.52

9.52 ppm to 10.35 ppm(answer)