2. (23 points) A survey is being designed to estimate the change in hours people worked per week over time. Assulne that the population of interest is very large so that taking a simple random sample without replacement is essentially the same as taking a simple random sample with replacement. Let. Y1,- be the number of hours Worked per wek for person i at time 1 and let ng be the number of hours worked per week for person 1' at time 2. Suppose that E[Y1.-] = athYm] = #2,Var(l'1;) = Var-{Ym} = 0'\". and aTT(Yll-5 YQI) = p. The goal is to estilnate #2 p1. Three sampling plans are considered as follows: Sampling plan 1: Independent random samples, each of size n, are chosen at times 1 and 2. Sampling plan 2: A single random sample of size n is chosen and the sampled individr uals are surveyed at both times 1 and 2. Sampling plan 3: A. random sample of m