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# HW 10 - Azfar Khandoker Dr Knapp Stat 350 4:30 HW#10 42 Ho...

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Azfar Khandoker Dr. Knapp Stat 350 4:30 HW #10 42. H o : π B = 0.4 , π E = 0.3 , π S = 0.2 , π A = 0.1 H A : π i is not the expected probability π B : The proportion of clients from the business statistics course. π E : The proportion of clients from the engineering statistics course. π S : The proportion of clients from the social science statistics course. π A : The proportion of clients from the agricultural statistics course. Course Business Engineering Social Science Agriculture Sum Observed 52 38 21 9 120 Expected 120(0.4) = 48 120(0.3) = 36 120(0.2) = 24 120(0.1) = 12 120 o - e2e 0.3333333 0.1111111 0.375 0.75 1.5964444 df = 4 – 1 = 3 , α = 0.05 therefore, χ 2 crtitical = 7.81 χ 2 = 1.5964444 therefore p -value = 0.666338 Since our p -value is greater than α = 0.05, we fail to reject H o that proportions of staffing are the expected values of π i . 44.

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H o : The i th location’s request proportion is equal to that location’s π i H A : The i th location’s request proportion is not equal to that location’s π i π i ’s: π 1 = . - - . = 5 5 1 5 530 130 π 2 = . - - . = 5 5 2 5 530 230 . . . π 10 = . - - . = 5 5 10 5 530 130 Location 1 2 3 4 5 6 7 8 9 10 Sum Observe d 4 15 32 25 38 31 32 14 10 8 200 Expected 6.66 7 13.33 3 20 26.66 7 33.33 3 33.33 3 26.66 7 20 13.3 3 6.66 7 200 o - e2e 1.06 7 0.208 3 7.2 0.104 2 0.653 3 0.163 3 1.066 7 1.8 0.83 3 0.26 7 13.36 df = 10 – 1 = 9 , α = 0.10 therefore χ 2 critical = 14.68 (16.91 for α = 0.05)
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HW 10 - Azfar Khandoker Dr Knapp Stat 350 4:30 HW#10 42 Ho...

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