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.)

Question

Sample Number Mean Std. Dev.
1 27 39 21
2 16 26 35

Lower Limit
Upper Limit

Answer 1

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)

Answer 2

Those was not the right answers, the ones that I had got previous was also close to them.

Answer 3

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)

Answer 4

Thanks, but those are wrong also.

Answer 5

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)