Suppose you take independent random samples from populations with means mu1 and mu2 and standard deviations sigma1 and sigma2. Furthermore, assume eit

tabita57i 2020-12-07 Answered

Suppose you take independent random samples from populations with means μ1andμ2 and standard deviations σ1andσ2. Furthermore, assume either that (i) both populations have normal distributions, or (ii) the sample sizes (n1 and n2) are large. If X1 and X2 are the random sample means, then how does the quantity
(x1x2)(μ1μ2)σ12n1+σ22n2
Give the name of the distribution and any parameters needed to describe it.

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Expert Answer

dessinemoie
Answered 2020-12-08 Author has 90 answers
Step 1
Given:
Two independent random samples from populations with
means-μ1andμ2
standard deviations - σ1andσ2
Assumptions:
i.Both populations have normal distributions
ii.The sample sizes(n1andn2) are large
Step 2 answer
X1andX2 are random samples then the quantity
t(say)=(x1x2)(μ1μ2)σ12n1+σ22n2
this quantity t(say)N(0,1) quantity t has standard normal distribution with mean zero and variance 1 the parameters are μ1μ2 is the difference between the population means and σ1andσ2 are the population standard deviations.
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