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# HW10 - 5(8.95 64 Anxious 11(10.91 10(14.03 8(4.05 29 13 93...

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Stat 415 HW 10 14.1 If no lane is preferred over another, the probability that a car will be driven in lane 1 , 2 , 3 , 4 is 1 4 . H 0 : p 1 = p 2 = p 3 = p 4 = 1 4 , H 1 : Some lanes were preffered over another X 2 = 4 X i =1 [ n i - E ( n i )] 2 E ( n i ) = ( n i - 250) 2 250 = 24 . 48 χ 2 3 where E ( n i ) = np i = 1000 ( 1 4 ) = 250 under H 0 . R = { X 2 7 . 81 = χ 2 3 , 0 . 05 } Thus we will reject the null hypothesis when X 2 is large. Also 24 . 48 > 12 . 8381 = χ 2 3 , 0 . 005 , so the p-value is less than . 005 . 14.5 H 0 : p 1 = . 69 , p 2 = . 21 p 3 = . 07 , p 4 = . 3 , H 1 : At least one of these probability is incorrect. User 1 2 3 4 n i 102 32 12 4 E ( n i ) 103.5 31.5 10.5 4.5 X 2 = 4 X i =1 [ n i - E ( n i )] 2 E ( n i ) = . 2995 χ 2 3 R = { X 2 7 . 81 = χ 2 3 , 0 . 05 } , p - value > . 95 . 2995 < χ 2 3 , 95 The null hypothesis is not rejected and we can not conclude that the figures given are inaccurate. 14.6 H 0 : p 1 = . 5 , p 2 = . 2 p 3 = . 2 , p 4 = . 1 , H 1 : At least one equality does not hold. n i 48 18 21 13 E ( n i ) 50 20 20 10 X 2 = 4 X i =1 [ n i - E ( n i )] 2 E ( n i ) = 1 . 23 χ 2 3 R = { X 2 7 . 81 = χ 2 3 , 0 . 05 } , p - value = 0 . 2541816 The null hypothesis is not rejected; there is no reason to suspect that the ratio is incorrect. i

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Stat 415 HW 10 14.10 a H 0 : p ij = p i p j , H 1 : p ij 6 = p i p j , i = 1 , 2 , j = 1 , 2 , 3 Pattern 0 - 3 hours 4 - 19 hour 20 - 54 hour Total Secure 24(24.09)
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Unformatted text preview: 5(8.95) 64 Anxious 11(10.91) 10(14.03) 8(4.05) 29 Total 35 45 13 93 X 2 = 6 X i =1 ( n i-E ( n i )) 2 E ( n i ) = 7 . 267 R = { X 2 ≥ 5 . 99 = χ 2 2 , . 05 } There is evidence of a dependence between attachment pattern and child care time. b The value X 2 = 7 . 267 is between χ 2 . 05 and χ 2 . 025 so that 0.25<p-value<0.05. The results are signiﬁcant. 14.17 a 20(13.44) 4(10.56) 8(14.56) 18(11.44) X 2 = 13 . 99 , R={ X 2 ≥ 3 . 84 } Reject H species segregate. b 4(10.56) 20(13.44) 18(11.44) 18(14.56) X 2 = 13 . 99 , R={ X 2 ≥ 3 . 84 } Reject H species are overly mixed. c 20(18.24) 4(5.76) 18(19.76) 8(6.24) X 2 = 13 . 99 , R={ X 2 ≥ 3 . 84 } Do not reject H . ii...
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