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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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 𝑑0=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 𝜇1 (eldest)
and 𝜇2 (youngest) with the same variance and their
difference is 𝑑=𝜇2−𝜇1.
(a) State proper testing hypotheses.
(b) Should we
use {𝑥¯𝑖,𝑠2𝑖}(𝑖=1,2){x¯i,si2}(i=1,2) or {𝐷¯,𝑠2𝑑}{D¯,sd2} for
testing? Explain your reason.
(c) Calculate the test statistic.
(d) Calculate the corresponding p-value.
(e) Draw your conclusion.