Question

Q11. The following table gives the hourly wages (in dollars) of fifteen randomly picked workers classified according to their occupations: Hourly wages of workers classified according to their occupations Plumber Electrician Painter Carpenter 17.6 18.5 16.8 17.4 18.3 18.7 16.7 16.5 17.6 17.7 16.6 16.8 18.3 16.4 17.8 Note: E2x7; = 4574.270 a) At a = 0.01 test whether the true mean wages differ for the four occupations.

Answer 1

solution The null and alternative hypothesis He: H: M = M₂ = M₂ = Mu at least two each other Mi's are different from The test statistic is F = MSB MSE Fp-1, N-P be tested where þ- N = Totel no. no. of means of observations Painter Carpenter Plumber Electrician 18.5 16.8 17.4 17.6 16.5 18.7 16.7 18.3 17.6 16.8 17.7 16.6 16.4 18.3 17.8 so.7 G= 261.7 91.0 66.5 Ti 53.5 2 261.7 Correction factor (C.F.) - a N 3+5+4+3 68486.89 IS 4565.79 eexij = 4574.270 Estij C.F. Total sum of squares (TSS) 4574.27 - 4565.79 8.48

Between sum of squares = -М - C.F. hi 66.5² 50.7² 53.5² 3 + 9 1² 5 + sest 507 3 - 4565.79 - 4572.68 - 4565.79 = 6.89 SSB borror sum of squares (SSE) = TSS- SSB = 8.48 -6.89 = 1.59 Mean sum of squares SSB MSB = þ-1 11 6.89 4-1 6.89 3 = 2.297 MSE $SE N-b. 1.59 = 0.145 1.59 15-4 The test statistic is MSB F MSE 2-297 0.145 = 15.84

of at denominator 3 6.22 to Ho if Fa;p-1,N-p Table value a=0.01 with numerator d. f and dif. 11 is Test is reject since cal E > we reject to conclude that the wages differ for four occupations 6.22 and mean the four
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