This is a question on a confidence interval for the difference between two popul

Question

This is a question on a confidence interval for the difference between two population means. According to the answer key, the answer for the 90 confidence interval is -549.82, -340:17. However, I do not seem to be getting the answer. Please help!

For each of the following exercises construct 90, 95, and 99 percent confidence intervals for the difference between population means. Where appropriate, state the assumptions that make your method valid. State the practical and probabilistic interpretations of each interval that you construct. Consider the variables under consideration in each exercise, and state what use you think researchers might make of your results Iannelo et al. (A-8) performed a study that examined free fatty acid concentrations in 18 lean subjects and i I obese subjects. The lean subjects had a mean level of 299 Eq/L with a standard error of the mean of 30, while the obese subjects had a mean of 744 Eq/L with a standard error of the mean of 62. 6.4.1.

Explanation / Answer

Sol;

alpha=1-0.9=0.1

alpha/2=0.1/2=0.05

df=n1+n2-2=18+11-2

Se of mean=30

s/sqrt(11)=30

s1=30*sqrt(18)=127.2792

s2=62*sqrt(11)=205.6307

Sp^2=((18-1)*127.2792^2+(11-1)*205.6307^2)/(18+11-2)

Sp=sqrt( 25860.73)

Sp=160.8127

Sp is pooled standard deviation

df=n1+n2-2=18+11-2=27

alpha=0.1

alpha/2=0.1/2=0.05

1-alpha/2=1-0.05=0.95

=T.INV(0.95;27)

=1.703288

t critical=1.703288

(299-744)+-1.703288*sqrt(160.8127^2/18+160.8127^2/11)

-445- 104.8274,-445+ 104.8274

-549.82.-340.17

lower limit= -549.82.

upper limit=-340.17

which is the given answer

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