Two random samples were selected independently from populations having normal di

Question

Two random samples were selected independently from populations having normal distributions. The following statistics were extracted from the samples x1 = 42.3 x2 = 32.4 If sigma1 = 3 and sigma2 = 2 and the sample sizes are n1 = 50 and n2 = 50, calculate a 95% confidence interval for the difference between the two population means. If sigma1 = sigma2, s1 = 3, and s2 = 2, and the sample sizes are n1 = 10 and n2 = 10, calculate a 95% confidence interval for the difference between the two population means. If sigma1 sigma2, S1 = 3, and s2 = 2, and the sample sizes are n1 = 10 and n2= 10, calculate a 95% confidence interval for the difference between the two population means.

Explanation / Answer

a)(x1-x2)=sqrt(1^2/n1+2^2/n2)

=.51

confidence interval at 95% will be

(42.3-32.4)-.51*1.96<1-2<(42.3-32.4)+.51*1.96

8.9<1-2<10.89

1.96 is z(.02)

b) Sp^2=((n1-1)*s1^2+(n2-1)*s2^2)/(n1+n2-2)

Sp^2=6.5

Sp=2.55

confidence interval at 95% will be

(42.3-32.4)-2.3*2.551/5<1-2<(42.3-32.4)+2.3*2.551/5

7.27<1-2<12.52

2.3 is t(.025,8)

c)

confidence interval at 95% will be

(42.3-32.4)-2.3*sqrt((s1^2/n1)+(s2^2/n2))<1-2<(42.3-32.4)-2.3*sqrt((s1^2/n1)+(s2^2/n2))

6.2<1-2<13.6

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