The assumption of equal variances, which was made in Exercise 8.41, is not always tenable. In such
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H0:μx = μY versus H1 : μx μY,
where we do not assume that Ï2x- Ï2Y, using the statistic
Where
The exact distribution of Tʹ is not pleasant, but we can approximate the distribution using Satterthwaite's approximation (Example 7.2.3).
(a) Show that
where v can be estimated with
(b) Argue that the distribution of Tʹ can be approximated by a t distribution with u degrees of freedom.
(c) Re-examine the data from Exercise 8.41 using the approximate t test of this exercise; that is, test if the mean age of the core is the same as the mean age of the periphery using the T' statistic.
(d) Is there any statistical evidence that the variance of the data from the core may be different from the variance of the data from the periphery? (Recall Example 5.4.1.)
The word "distribution" has several meanings in the financial world, most of them pertaining to the payment of assets from a fund, account, or individual security to an investor or beneficiary. Retirement account distributions are among the most...
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