A laboratory testing of five samples on the content of a cer

A laboratory testing of five samples on the content of a certain water-quality indicator results in the following values: 3.41, 3.06. 2.94, 3.27, and 3.32 mg/L. Find the 95% confidence interval for the mean content of this indicator. What assumptions are made?

Solution

f(x) = |x| and g(x) = 7/(x^2 +7)

a).

(fog)(4) = f[g(4)]

=f[7/(4^2 +7) ]

=f[ 7/16+7)

=f(7/23)

= 7/23

b).

(gof)(2) = g[f(2)]

=g(2)

= 7/(2^2+7)

= 7/(4+7)

=7/11

c).

(fof)(1) = f[f(1)]

=f(1)

=1

d).

(gog)(0) =g[g(0)]

=g(7/7)

=g(1)

= 7/(1^2+7)

=7/8