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### hw7.4

Course: STAT 583, Fall 2008
School: Rutgers
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7.4 Section (p.409) ^ Since = X n , it follows from equation (6) that n 1 / 2 1/ 2 1/ 2 ^ ^ Pr( &gt; + k ) = Pr U &gt; kn = Pr(U &gt; ( n - 1) k ) = Pr(U &gt; 4k ) = 0.95 n - 1 where U has a t distribution with n1 = 16 degrees of freedom. Note that Pr(U 4k) = 1 Pr(U &gt; 4k) = 0.05. From table of t distribution 4 (p.692), k = 1.746, k = 0.4365. 3. Let Y = ( X 1 + X 2 ) /...

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7.4 Section (p.409) ^ Since = X n , it follows from equation (6) that n 1 / 2 1/ 2 1/ 2 ^ ^ Pr( > + k ) = Pr U > kn = Pr(U > ( n - 1) k ) = Pr(U > 4k ) = 0.95 n - 1 where U has a t distribution with n1 = 16 degrees of freedom. Note that Pr(U 4k) = 1 Pr(U > 4k) = 0.05. From table of t distribution 4 (p.692), k = 1.746, k = 0.4365. 3. Let Y = ( X 1 + X 2 ) / 2 , then it has a standard normal distribution. Let 2. , then it has a 2 distribution with 3 degrees of freedom. Note also that Y and Z are independent. Therefore, Y/(Z/3)1/2 has a t distribution. So c = 3 / 2 . 2 Z = X 32 + X 4 + X 52
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