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4. Let X1, X2, X3, X, be a random sample of STAT2601 scores, assumed to be N (4z, o), and let Y1, Y2, Y3, Y4, Y, be a random sample of STAT2602 scores, assumed to be N(ty, o). Suppose X1, X2, X3, X4, Y, Y2, Y3, Ya, Ys are independent, and the fol- lowing data are observed: * = 75 2 = 95 a = 80 4 = 65 Y1 = 80 2 = 75 ys =90 y = 70 y5 = 70 %3D (i) Find a 90% confidence interval estimate for o. (ii) Find a 90% confidence interval estimate for o?/o. (X-Xa)*/a (Y - Y)?/o? (iii) Find the distribution of

4. Let X1, X2, X3, X, be a random sample of STAT2601 scores, assumed to be N (4z, o), and let Y1, Y2, Y3, Y4, Y, be a random sample of STAT2602 scores, assumed to be N(ty, o). Suppose X1, X2, X3, X4, Y, Y2, Y3, Ya, Ys are independent, and the fol- lowing data are observed: * = 75 2 = 95 a = 80 4 = 65 Y1 = 80 2 = 75 ys =90 y = 70 y5 = 70 %3D (i) Find a 90% confidence interval estimate for o. (ii) Find a 90% confidence interval estimate for o?/o. (X-Xa)*/a (Y - Y)?/o? (iii) Find the distribution of

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 31E
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4. Let X1, X2, X3, X, be a random sample of STAT2601 scores, assumed to be N (H2, o), and let Y1, Y2, Y3, Y4, Y, be a random sample of STAT2602 scores, assumed to be N(Hy, o). Suppose X1, X2, Xa, X4, Y, Y2, Ys, Y4, Ys are independent, and the fol- lowing data are observed: * = 75 r = 95 3 = 80 4 = 65 Y = 80 2 = 75 Ys = 90 y = 70 ys = 70 %3D (i) Find a 90% confidence interval estimate for o. (ii) Find a 90% confidence interval estimate for o/o. (X - Xa)*/o (Yi - Y2) /o (iii) Find the distribution of (iv) Based on the result in (iii), construct an alternative 90% confidenc interval estimate for o/o (v) Is the confidence interval estimate in (ii) better than the one in (iv)? Expli- your answer.
Transcribed Image Text:4. Let X1, X2, X3, X, be a random sample of STAT2601 scores, assumed to be N (H2, o), and let Y1, Y2, Y3, Y4, Y, be a random sample of STAT2602 scores, assumed to be N(Hy, o). Suppose X1, X2, Xa, X4, Y, Y2, Ys, Y4, Ys are independent, and the fol- lowing data are observed: * = 75 r = 95 3 = 80 4 = 65 Y = 80 2 = 75 Ys = 90 y = 70 ys = 70 %3D (i) Find a 90% confidence interval estimate for o. (ii) Find a 90% confidence interval estimate for o/o. (X - Xa)*/o (Yi - Y2) /o (iii) Find the distribution of (iv) Based on the result in (iii), construct an alternative 90% confidenc interval estimate for o/o (v) Is the confidence interval estimate in (ii) better than the one in (iv)? Expli- your answer.
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