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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 - ,

    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)

  • math - ,

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

  • math - ,

    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)

  • math - ,

    Thanks, but those are wrong also.

  • math - ,

    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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