Question

How is the test statistic for a claim about 2 population means, independent samples, standard deviations unknown, similar to the test statistic for 1 population mean, standard deviation unknown?

Answer 1

Solution

t test for difference in means ,as standard deviations are unknown.

If they specify variances are equal

That is if the given sample standard deviations are equal use

pooled standard deviation

t = (xlbar – x2bar) – (ul - M2))/Sp* 1/n1+1/n2

where

Sp = V(nl - 1) * $12 + (n2 - 1) * $22/(n1 + n2 - 2))

If they dont specificy anything that

use

t = (xlbar – xabar)/(s12 /nl + s22 /n2)

where x1bar=sample mean of group1

s1^2=sample variance of group 1

n1=sample size of group1

x2bar=sample mean of group2

s2^2=sample variance of group2

n2=sample size of group2