Mth562-HW8-4

Mth562-HW8-4 - MTH/STA 562 Exercise 8.17. The point...

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MTH/STA 562 Exercise 8.17 . The point estimate of is b = Y = 11 : 5. With n = 50 and S = 3 : 5, a bound on the error of estimation is 2 ± Y = 2 ± p n 2 (3 : 5) p 50 = 0 : 99 : Exercise 8.18 . The point estimate of is b = Y = 7 : 2. With n = 200 and S = 5 : 6, a bound on the error of estimation is 2 ± Y = 2 ± p n 2 (5 : 6) p 200 = 0 : 79 : Exercise 8.19 . ( a ) The point estimate of is b = Y = 11 : 3. With n = 467 and S = 16 : 6, a bound on the error of estimation is 2 ± Y = 2 ± p n 2 (16 : 6) p 467 = 1 : 54 : ( b ) The point estimate of R ± C is Y R ± Y C = 46 : 4 ± 45 : 1 = 1 : 3. With n R = 191, n C = 467, S R = 9 : 8, and S C = 10 : 2, a bound on the error of estimation is 2 ± Y R Y C = 2 s ± 2 R n R + ± 2 C n C 2 s S 2 R n R + S 2 C n C = 2 s (9 : 8) 2 191 + (10 : 2) 2 467 = 1 : 7 : ( c ) The point estimate of p C ± p R is b p C ± b p R = 0 : 78 ± 0 : 61 = 0 : 17. A bound on the error of estimation is 2 ± b p C b p R = 2 s p C (1 ± p C ) n C + p R (1 ± p R ) n R 2 s b p C (1 ± b p C ) n C + b p R (1 ± b p R ) n R = 2 s (0 : 78) (0 : 22) 467 + (0 : 61) (0 : 39) 191 = 0 : 08 : Exercise 8.20 . The point estimate of p is b p = 0 : 54. A bound on the error of estimation is 2 ± b p = 2 s p (1 ± p ) n 2 s b p (1 ± b p ) n = 2 s (0 : 54) (0 : 46) 1000 = 0 : 03 : Note that 054 > 0 : 50. Thus, we can conclude that a majority of individuals in this age group feel that religion is a very important part of their lives.
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Exercise 8.21 . The point estimate of 1 2 is Y 1 Y 2 = 2 : 4 3 : 1 = & 0 : 7. With n 1 = n 2 = 100, S 2 1 = 1 : 44, and S 2 2 = 2 : 64, a bound on the error of estimation is 2 ± Y 1 Y 2 = 2 s ± 2 1 n 1 + ± 2 2 n 2 ± 2 s S 2 1 n 1 + S 2 2 n 2 = 2 s 1 : 44 100 + 2 : 64 100 = 0 : 404 : Exercise 8.22 . The point estimate of p is b p = 2
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Mth562-HW8-4 - MTH/STA 562 Exercise 8.17. The point...

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