Last year, those who took the LSAT a second time score an average of 2.8 points higher than the first time. Suppose two

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Last year, those who took the LSAT a second time score anaverage of 2.8 points higher than the first time. Suppose twoindependent and identically distributed random samples are drawnfrom this year’s exam: first-time and second- time LSATtakers. Must solve all parts using de-standardize tofind dHC and dLC.
a) Write the hypothesis test where the null is that thedifference in scores between first- and second-time LSAT takers hasnot changed since last year and a two-sided alternative.
b) Suppose two independent random samples are drawn. One randomsample contains the LSAT scores of first-time takers and has 25observations and a sample variance of 256. The other random samplecontains the LSAT scores of second-time takers and has 16observations and a sample variance of 144. Derive the rejectionrule at 𝛼 = 0.20 of the test in part a).
Please show how to get variance and t.