1. Suppose the GRE scores of 25 pairs of eldest and youngest
siblings are analyzed to see whether the youngest group's scores
are at least π0=2d0=2 points better than the eldest
group's score, where group 1 are the eldest children and group 2
are the youngest children. Assume that the scores in both groups
are normal with the means π1 (eldest)
and π2 (youngest) with the same variance and their
difference is π=π2βπ1.
(a) State proper testing hypotheses.
(b) Should we
use {π₯Β―π,π 2π}(π=1,2){xΒ―i,si2}(i=1,2) or {π·Β―,π 2π}{DΒ―,sd2} for
testing? Explain your reason.
(c) Calculate the test statistic.
(d) Calculate the corresponding p-value.
(e) Draw your conclusion.
1. Suppose the GRE scores of 25 pairs of eldest and youngest siblings are analyzed to see whether the youngest group's s
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