Question

In an investigation of toxins produced by molds that infect corn crops, a biochemist prepares extracts of the mold culture with organic solvents and then measures the amount of the toxic substance per gram of solution. From 11 preparations of the mold culture, the following 90% confidence interval for the average amount of the toxic substance per gram of solution was produced, (1.28, 1.64). What was the sample standard deviation?

Answer 1

In general, (1-)% confidence interval for population mean is obtained as follows :

( Student's t-distribution is used since this experiments consists of small sample)

i.e.    E ( where E = )

i.e. Lower limit = - E = 1.28   and Upper limit =   + E = 1.64
And Upper limit - Lower limit =   + E - (  ​​​​​​​ - E ) = 2*E
1.64 - 1.28 = 2*
Here, t( /2, n-1 ) = t( 0.05, 10 ) = 1.812461 and n = 11

S = 0.18 / ( 2*1.812461*sqrt(1/11) ) = 0.32938

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