What is the distribution of the t-test statistic if m, n -----> ∞ ?

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
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What is the distribution of the t-test statistic if m, n -----> ∞ ?

6. Suppose that X1, ..., Xm form a random sample from
the normal distribution with unknown mean µ1 and un-
known variance o?, and Y1, ..., Y, form an independent
random sample from another normal distribution with un-
known mean µz and the same unknown variance o?. For
each constant (-00 <1 < o0), construct a t test of the
following hypotheses with m +n – 2 degrees of freedom:
Ho: 41- 42 =1,
H¡: µ1– 42 # 1.
Transcribed Image Text:6. Suppose that X1, ..., Xm form a random sample from the normal distribution with unknown mean µ1 and un- known variance o?, and Y1, ..., Y, form an independent random sample from another normal distribution with un- known mean µz and the same unknown variance o?. For each constant (-00 <1 < o0), construct a t test of the following hypotheses with m +n – 2 degrees of freedom: Ho: 41- 42 =1, H¡: µ1– 42 # 1.
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