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Lot X, Y, S2chi, S2gamma be the respective sample means and unbiased estimates o

ID: 2942963 • Letter: L

Question

Lot X, Y, S2chi, S2gamma be the respective sample means and unbiased estimates of the variances using samples of sizes n and m from the independent normal distributions N(mu chi, sigma2gamma) and N(mu gamma, sigma2gamma), where all the parameters are unknown. If however sigma2chisigma2gamma = d, a known constant, then assuming following to be true (X - Y) - (mu chi-mu gamma)/ d sigma2gamma/n +sigmma2gamma/m (n-1)S2chi/d sigma2gamma +(m-1)S2gamma/sigma2gamma~chi(n +m-2) The above two random variables are independent. Obtain a random variable that has t-distribution and can be used to construct a confidence interval for mu chi - mu gamma, Find the (1 - alpha )100% confidence interval.

Explanation / Answer

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