Posted by **Tracy** on Wednesday, June 26, 2013 at 5:07pm.

Find the 95% confidence interval for the difference between two means based on this information about two samples. Assume independent samples from normal populations. (Use conservative degrees of freedom.) (Give your answers correct to two decimal places.)

Sample Number Mean Std. Dev.

1 27 39 21

2 16 26 35

Lower Limit

Upper Limit

- math -
**Eli**, Wednesday, June 26, 2013 at 8:39pm
xbar1 - xbar2 -+ ta/2 * sqrt(s1^2/n2 + s2^2/n2)

13 -+ 2.02* sqrt(21^2/27 + 35^2 /16))

(-6.47, 32.47)

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**Tracy**, Wednesday, June 26, 2013 at 9:30pm
Those was not the right answers, the ones that I had got previous was also close to them.

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**Eli**, Wednesday, June 26, 2013 at 10:05pm
For pooled

sp = (n1-1)s1^2 + (n2-1)s2^2 /(n1+n2-2)

Sqrt(29841/41 )

= 26.978

Confidence interval

The degrees of freedom of t is n1+ n2 -2

xbar1-xbar2 -+ta/2 *sp*sqrt(1/n1 +1/n2))

(39-26)-+ 2.02* 26.978sqrt(1/27+ 1/16))

(-4.19, 30.19)

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**Tracy**, Wednesday, June 26, 2013 at 11:00pm
Thanks, but those are wrong also.

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**Kuai**, Thursday, June 27, 2013 at 4:12pm
conservative degrees of freedom, you use small number. Df = 15

(39-26)-+ 2.13* sqrt(21^2/27 + 35^2/16))

13 -+ 2.13*sqrt(4459/48)

13 -+ 20.53

(-7.53, 33.53)

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