RVUC- Statistics Short Note (2).doc

# Msw msb f the f distribution characteristics of f

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MSW MSB F The F-Distribution Characteristics of F-distribution It is a continuous probability distribution It is uni-modal It has two parameters; pair of degrees of freedom, ν 1 and ν 2 o ν 1 = the number of degrees of freedom in the numerator of F-ratio; ν 1 = k – 1 o ν 2 = the number of degrees of freedom in the denominator of F-ratio; ν 2 = n T - k It is a positively skewed distribution, and tends to get more symmetrical as the degrees of freedom in the numerator and denominator increase. 1. The mean for an F-distribution is , 2 2 2 for ν 2 > 2; and the standard deviation is 4 2 2 2 2 2 2 1 2 1 2 2 for ν 2 > 4. Illustration: A cement manufacturing company is considering building a new plant at one of the four different cities in Ethiopia. One of the important factors in the decision is the annual construction permit of the four cities. Suppose that, in a preliminary study, the number of construction permits is identified. The results are shown in the accompanying table below. Is there sufficient evidence to conclude that differences exist in the average annual construction permit among the four cities? Use α = 0.01. Adama Hawassa Robe Nekempte 25 32 27 18 27 35 32 23 21 30 48 29 27

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28 | P a g e 17 46 25 26 29 32 20 42 30 22 12 19 18 51 27 159 294 182 138 1 X = 26.50 2 X = 32.67 3 X = 26.00 4 X = 27.60 X = 28.63 2 1 S = 26.30 2 2 S = 107.5 2 3 S = 136.33 2 4 S = 81.30 Solution 1. Ho: μ 1 = μ 2 = μ 3 = μ 4 μ 1 , μ 2 , μ 3 and μ 4 are not all equal 2. α = 0.01 ν 1 = K – 1 ν 2 = n T – k F 0.01 , 3,23 = 4.76 = 4 - 1 = 3 = 27 – 4 = 23 Reject Ho if sample F > 4.76 3. Sample F MSB = 1 4 63 . 28 60 . 27 5 63 . 28 00 . 26 7 63 . 28 67 . 32 9 63 . 28 5 . 26 6 1 2 2 2 2 2 K X X n j j 95 . 75 3 84 . 227 MSW = 81 . 92 23 68 . 2134 4 27 3 . 81 4 33 . 136 6 5 . 107 8 3 . 26 5 1 2 1 K n S n T j 82 . 0 81 . 92 95 . 75 MSW MSB F 4. Do not reject Ho. No difference exists in the average annual construction permit among the four communities. 28
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