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Unformatted text preview: MTH/STA 562 Exercise 8.81 . Calculate n X i =1 Y i = 514 : 4 and n X i =1 Y 2 i = 44 ; 103 : 74 with n = 6. Then Y = 1 n n X i =1 Y i = 514 : 4 6 = 85 : 73 and S 2 = 1 n & 1 n X i =1 Y 2 i & n Y 2 ! = 44 ; 103 : 74 & 6 (85 : 73) 2 5 = 0 : 502667 : With con&dence coecient 1 & & = 0 : 90 and n & 1 = 5 degrees of freedom, we read from Table 5 that 2 1 & &= 2 = 2 : 95 = 1 : 145476 and 2 &= 2 = 2 : 05 = 11 : 0705. Hence, the 90% con&dence interval for 2 is 5 (0 : 502667) 11 : 0705 < 2 < 5 (0 : 502667) 1 : 145476 or 0 : 227 < 2 < 2 : 194. Exercise 8.82 . Calculate n X i =1 Y i = 608 and n X i =1 Y 2 i = 37 ; 538 with n = 10. Then Y = 1 n n X i =1 Y i = 608 10 = 60 : 8 and S 2 = 1 n & 1 n X i =1 Y 2 i & n Y 2 ! = 37 ; 538 & 10 (60 : 8) 2 9 = 571 : 6 : With con&dence coecient 1 & & = 0 : 90 and n & 1 = 9 degrees of freedom, we read from Table 5 that 2 1 & &= 2 = 2 : 95 = 3 : 32511 and 2 &= 2 = 2 : 05 = 16 : 9190. Hence, the 90% con&dence interval for 2 is 9 (571 : 6) 11 : 0705 < 2 < 9 (571 : 6) 16 : 9190 or 33...
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This note was uploaded on 04/20/2008 for the course MTH 562 taught by Professor Cheng during the Spring '08 term at Creighton.
 Spring '08
 Cheng

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