Question

XII. a. Find the critical values for a 90% confidence interval using the chi-square distribution with df = 15 b. Now construct the 90% confidence interval with s? = 55.5 and n=16, df = 15.

Answer 1

XI am Here I giving you the combindd solation bor q. a & S. 6 Here we construct 90 % confidence interval bor oor Here we use the xt - vociate as pivotal quantity, z(x; -x)" (n-1) s? X{n-1) or Take two constants Xin-1), 412 and xin-1), (1-4/2). such that. • Xu-), (-4/2) x² < Xn-1), 4/2 ] =10 (1-4) 100) 242 4/2 Co I Wh

Now, [x (n-1) sr in-1), (-12) X 2, 4/2] = 1-0. ar P[ xin-i), (-1/2) vl at Jan), ar J =12 (n)S (n-1) Sr او (1-2) Wils" a VI J. X (n-1), ali Xn-1), (1-4/2) ای (1) ore (n-1) SL J. X_n-1), ah xn-), (-2/2) 1- x=0.90 3) a =0.10 X/2 = 0.05 xis, 15,0.05 24.9958 Xis, 0.95 = 7.2609 15 x 55.5 an el 15 x 55.5 7.2609 24.9958 (33. 33.3056, 11416552)
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