M562-HW8-8

# M562-HW8-8 - MTH/STA 562 Exercise 8.68. It is given that Y...

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MTH/STA 562 Exercise 8.68 . It is given that Y = 26 : 6, S = 7 : 4, and n = 21. For a 95% n 1 = 20 degrees of freedom, t 0 : 025 = 2 : 086. Then a 95% is Y ± t 0 : 025 S p n = 26 : 6 ± 2 : 086 7 : 4 p 21 = 26 : 6 ± 3 : 37 or (23 : 33 ; 29 : 97). Exercise 8.69 . 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 = 63 : 5111 : n 1 = 9 degrees of freedom, t 0 : 025 = 2 : 262. Then is Y ± t 0 : 025 S p n = 60 : 8 ± 2 : 262 r 63 : 5111 10 = 60 : 8 ± 5 : 701 or (55 : 099 ; 66 : 501). Exercise 8.70 . ( a ) It is given that Y = 419, S = 57, and n = 20. For a 90% n 1 = 19 degrees of freedom, t 0 : 05 = 1 : 729. Then a 90% is Y ± t 0 : 05 S p n = 419 ± 1 : 729 57 p 20 = 419 ± 22 : 04 or (396 : 96 ; 441 : 04). ( b for example, are also believable values for . ( c ) It is given that Y = 455, S = 69, and n with n 1 = 19 degrees of freedom, t 0 : 05 = 1 : for is Y ± t 0 : 05 S p n = 455 ± 1 : 729 69 p 20 = 455 ± 26 : 67 or (428 : 33 ; 481 : SAT score

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Exercise 8.71 . ( a ) It is given that Y 1 = 14 : 5, Y 2 = 11 : 1, S 1 = 3 : 92, S 2 = 3 : 98, and n 1 = n 2 = 10. Then S 2 p = ( n 1 1) S 2 1 + ( n 2 1) S 2 2 n 1 + n 2 2 = 9 (3 : 92) 2 + 9 (3 : 98) 2 18 = 15 : 6034 : For a 95% con±dence level with n 1 + n 2 2 = 18 degrees of freedom, t 0 : 025 = 2 : 101. Then a 95% con±dence interval for is Y 1 Y 2 ± ± t 0 : 025 S p r 1 n 1 + 1 n 2 = (14 : 5 11 : 1) ± 2 : 101 s 15 : 6034 ² 1 10 + 1 10 ³ = 3 : 4 ± 3 : 7 or ( & 0 : 3 ; 7 : 1). ( b
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## M562-HW8-8 - MTH/STA 562 Exercise 8.68. It is given that Y...

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