: Let x1, X2, ..., Xn, Xn+1 be a random sample of size n + 1,n > 1, from a distribution E (xi-x)2 that is N(u, o2). Let i = and S2 = Find the constant c so that the statistic n п-1 c(x-xn+1) has a t-distribution. If n = 8, determine k such that S P(x - ks < xg < i+ ks) = 0.80. The observed interval ( - kS,x + kS) is often called an 80% prediction interval for x,.

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