Question

Construct a 90% confidence interval for a ratio of population variances. Assume that the random samples have been taken from normal distributions. n1 = 21 X = 23 S1 = 3.6 n2 = 28 X2 = 27 S1 = 3.3 <

Answer 1

given: ni=21 n28 O 7=23 81₂=27 S,=3.6 {=3.3 To fint: 90% confitence Interval for Ratio population variances. Solution I let F be f-statietic with tegree of free tom ni-l and Mel. then (100-2% confitence Interval for ratio of variances is given by S, M-1 May 6/63 Si Falal S₂) Fahrlinet Sz here too-d=90) 2 =10%=0.1 ant allo n = 21 and n₂ =28 = 90% Colo is Si 'Si S₂ 9.05, cue hable from F table F0.05,20,27 = 1.97 1 (Fogs,20,27 0.05, 20, 27

2 1 = 3.6 ant 52=3.3 6/6,12 is also =) 90% (.Jo il - (0.6041, 2.3443), Done = 13.6 3.3 13.6 3.3 1.97 1.97
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