hw7solution[1]

hw7solution[1] - Hw 7 Solution 4 6 7 13(SAS 16(SAS 21a(SAS...

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Hw 7 Solution 4, 6, 7, 13(SAS), 16(SAS), 21a(SAS), 24, 25, 28(SAS) 4. H 0 : Distribution is 10%, 20%, 40%, 20%, 10% H 1 : H 0 is false α = 0.05 E ) E - (O Σ = χ 2 2 , df=4 Reject H 0 if χ 2 > 9.49 1 2 3 4 5 Total Observed 12 18 50 10 10 100 Expected 10 20 40 20 10 100 (O-E) 2 /E 0.4 0.2 2.5 5 0 8.1 χ 2 = 8.1 Do not reject H 0 since 8.1 < 9.49. We do not have significant evidence, α =0.05, to show that the distribution is not 10%, 20%, 40%, 20%, 10%. 6. H 0 : Distribution is 25%, 25%, 50% H 1 : H 0 is false α = 0.05 E ) E - (O Σ = χ 2 2 , df=2 Reject H 0 if χ 2 > 5.99 R C L Total Observed 205 220 575 1000 Expected 250 250 500 1000 (O-E) 2 /E 8.1 3.6 11.25 22.95 χ 2 = 22.95 Reject H 0 since 22.95 > 5.99. We have significant evidence, α =0.05, to show that the distribution is not 25%, 25%, 50%, p<0.005. 7. H 0 : p = 0.15 H 1 : p > 0.15 α = 0.05 n ) p - (1 p p - p ˆ = Z 0 0 0 Check: min(np 0 , n(1-p 0 ))=min(125(0.15),125(0.85))=18.75 Reject H 0 if Z > 1.645 0.20 = 125 25 = n x = p ˆ
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125 0.15) 0.15(1 0.15 0.20 n ) p - (1 p p - p ˆ = Z 0 0 0 - - = =0.05/0.032 = 1.57 Do not reject H 0 since 1.57 < 1.645. We do not have significant evidence, α =0.05, to show that p > 0.15. 13. n=200 p ˆ = 0.60 a) n ) p ˆ (1 p ˆ Z p ˆ α/2 - 1 - ± Check: min(n p ˆ ,n(1- p ˆ ))=min(200(0.60), 200(0.40))=80 0.60 + 0.068 (0.532, 0.668) b) H 0 : p = 0.70 H 1 : p 70 α = 0.05 n ) p - (1 p p - p ˆ = Z 0 0 0 Check: min(np 0 , n(1-p 0 ))=min(100(0.70),100(0.70))=30 Reject H 0 if Z > 1.960 or if Z < -1.960 100 0.70) 0.70(1 0.70 0.72 n ) p - (1 p p - p ˆ = Z 0 0 0 - - = =0.02/0.046 = 0.44 Do not reject H 0 since –1.960 < 0.44 < 1.960.
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