Let two independent random samples, each of size 10, from two normal distributions N(mu_1, sigma_2) and N(mu_2, sigma_2) yield x = 4.8, s_1^2 = 8.64, y = 5.6, s_2^2 = 7.88. Find a 95% confidence interval for mu_1 − mu_2.

Haven 2021-02-04 Answered
Let two independent random samples, each of size 10, from two normal distributions N(μ1,σ2)andN(μ2,σ2) yield x=4.8,s12
=8.64,y=5.6,s22
= 7.88.
Find a 95% confidence interval for μ1μ2.
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Expert Answer

l1koV
Answered 2021-02-05 Author has 100 answers

Step 1
A100(1α)% confidence interval on the difference is
x1x2tα2,n1+n21sp1n1+1n2μ1μ2x1x2,+tα2,n1+n21sp1n1+1n2
where sp=(n11)s12+(n21)s22n1+n21
Step 2
Considering 95% confidence interval,
α=0.05
x1=4.8
x2=5.6
s12=8.64
s22=7.88
n1=10
n2=10
Therefore
tα2,n1+n21=t0.052,10+101
=t0.025,19
=2.093
Step 3
To calculate sp
sp=(n11)s12+(n21)s22n1+n21
sp=((101)8.64+(101)7.8819)
sp=2.797
Step 4
Now, by substituting all the values in the equation, we get
x1x2tα2,n1+n21sp1n1+1n2μ1μ2x1x2

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