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stats 363 HW 8-7 - Section 8.7 Exercise 8.51 given by A 90...

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Section 8.7 Exercise 8.51 . A 90% con°dence interval for p 1 ° p 2 is approximately given by ( b p 1 ° b p 2 ) ± 1 : 645 s b p 1 b q 1 n 1 + b p 2 b q 2 n 2 . ( a ) If n 1 = 800, n 2 = 640, x 1 = 337, x 2 = 374, then b p 1 = x 1 n 1 = 337 800 = 0 : 421 and b p 2 = x 2 n 2 = 374 640 = 0 : 584 : Hence, the interval is (0 : 421 ° 0 : 584) ± 1 : 645 s (0 : 421) (0 : 579) 800 + (0 : 584) (0 : 416) 640 = ° 0 : 163 ± 0 : 043 or ° 0 : 206 < p 1 ° p 2 < ° 0 : 120 : ( b ) The sampling distribution of b p 1 ° b p 2 can be approximated by a normal distribution with n 1 b p 1 > 5, n 1 b q 1 > 5, n 2 b p 2 > 5, and n 2 b q 2 > 5. Exercise 8.53 . A 95% con°dence interval for p 1 ° p 2 is approximately given by ( b p 1 ° b p 2 ) ± 1 : 96 s b p 1 b q 1 n 1 + b p 2 b q 2 n 2 . ( a ) If n 1 = 56, n 2 = 32, x 1 = 12, x 2 = 8, then b p 1 = x 1 n 1 = 12 56 = 0 : 214 and b p 2 = x 2 n 2 = 8 32 = 0 : 250 : Hence, the interval is (0 : 214 ° 0 : 250) ± 1 : 96 s (0 : 214) (0 : 786) 56 + (0 : 250) (0 : 750) 32 = ° 0 : 036 ± 0 : 185 or ° 0 : 221 < p 1 ° p 2 < 0 : 149 : ( b ) No, because the interval contains the value p 1 ° p 2 = 0. Exercise 8.55 . A 99% con°dence interval for p 1 ° p 2 is approximately given by ( b p 1 ° b p 2 ) ± 2 : 575 s b p 1 b q 1 n 1 + b p 2 b q 2 n 2 .
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