hypothesis 4b

Mr. Leung ka kit
Ho: The number of votes for Mr. leung ka kit is less than or equal to 20%.
Ha: The number of votes for Mr. leung ka kit is greater than 20%. (right tailed test)

p' = 0.18
p = 0.2
q = 0.8
z test value: (0.18 - 0.2) / (0.2*0.8/1000)^1/2 = -1.58

z critical value at sign. level 0.05 = +1.65 (right tailed test should be in + sign)
the test value is in - sign

i would say that the hypothesis is not valid
they are in different sign, so thats why i say that the hypothesis is not valid
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Mr. Donald Tsang
Ho: The number of votes for Mr. Donald Tsang is greater or equal to 60%.
Ha: The number of votes for Mr. Donald Tsang is less than 60%.

p' = 0.58
p = 0.6
q = 0.4

z test value : (0.58 - 0.6) / (0.6*0.4/1000)^1/2 = - 1.29

z critical values at sign. level 0.05 is -1.65 (left tailed test, which is in - sign)

I would say the hypothesis is valid

the decision is not to reject Ho, and we conclude that he number of votes for Mr. Donald Tsang is greater or equal to 60%.

Both hypotheses are valid.

For Leung Ka Kit,
H0: p0 <= 0.2, where <= denoted as less than or equal to
Ha: p0 > 0.2
sample population ps=X/n=180/1000=0.18

Z = (ps-p0)/sqrt[p0*(1-p0)/n]
Z = (0.18-0.2)/sqrt[0.2*(1-0.2)/1000]= -0.02/0.0126491106 = -1.58113883,
which is not greater than the critical value, 1.645
so, we do NOT reject H0 and p0 is less than or equal to 0.2.



For Donald Tsang,
H0: p1 >= 0.6, where >= denoted as greater than or equal to
Ha: p1 < 0.6
sample population ps=X/n=580/1000=0.58

Z = (ps-p1)/sqrt[p1*(1-p1)/n]
Z = (0.58-0.6)/sqrt[0.6*(1-0.6)/1000]= -0.02/0.0154919334 = -1.290994449,
which is not less than the critical value, -1.645
so, we do NOT reject H0 and p1 is greater than or equal to 0.6

2007-04-12 09:28:33 補充：
Due to different answers, I now check the P-value for Leung Ka Kit's population.P(Z>-1.58)=P(Z<1.58)=0.9429 > significance level 0.05In this case, however, we may have a large Type II error."& lt" = "<""& gt" = ">"