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STAT 4290 April 20 2011

# STAT 4290 April 20 2011 - Example F0(x discrete uniform on...

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Example F0(x) – discrete uniform on the integers 1, 2, 3, 4, 5 n = 10, observe the values 1,1,1,2,2,2,3,3,3,3 Ho: population distribution is Fo(x) H1: Not Ho Draw the cumulative probability of Fo(x) and S(x) D_obs = sup| Fo(x) – S(x) | = 0.4 at x =3 We want to find the associate p-value Find P(D+ >= 0.4) n(1-D_obs) = 6, so we need to find f0, f1,…f5 The horizontal line with ordinate 1 – D_obs = 1- 0.4 = 0.6 intersects Fo(x) right at the top of the jump at x=3,so fo = 0.6 The horizontal line with ordinate 1-0.4-0.1 = 0.5 intersects Fo(x) at a jump, so f1 = equals the height of Fo(x) at the bottom of the jump i.e., 0.4. Likewise f2=0.4, f3=f4=0.2, f5=0 Then e_0 = 1, e_1=1-0.6=0.4 e_2=0.32 e_3=0.208 e_4=0.295 P(D+ >=0.4) = long painful calculation = 0.021 P(D>= 0.4) = P(D+ >=0.4)+ P(D- >=0.4) = 0.042 At level alpha = 0.05. He reject ho Note: If we had use Table A13, n=10, alpha=0.05, two-sided test, the critical value is 0.409>0.4 => Don’t reject Ho.

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We can also use the Kolmogorov test statistic to get confidence bands for the distribution function as a whole: IMPORTANT POINT Up until now, we’ve been using a completely specified
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STAT 4290 April 20 2011 - Example F0(x discrete uniform on...

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