> I have 2 independent samples and the standard errors and n's associated
with
> each of them. If a and b are constants, what is the formula for the 95%
> confidence interval for (a(Xbar1)+b(xbar2))?
Presumably you mean "95% c.i. for (a(mu1) + b(mu2))"? (Xbar1 is a random
variable not a parameter and xbar2 is just a number.)
Assuming X1 and X2 are both normal and have the same variance (I haven't got
a clue how to proceed otherwise) then
[ (a(Xbar1) + b(Xbar2)) - (a(mu1) + a(mu2)) ]
times
sqrt(n1 + n2 -2)
divided by
sqrt(a*a/n1 + b*b/n2)
all divided by
sqrt((n1-1)*s1*s1 + (n2-1)*s2*s2)
is distributed as t(n1 + n2 - 2)
and the c.i. follows from that.
Any help?
Fergus
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