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: ΣΣx2ij=4574.270ΣΣxij2=4574.270
a) At α=0.01 test whether the true mean wages differ for the four occupations.

b) State the assumption(s) required for the test.

Answer 1

a) The null and alternative hypotheses are: HO: uli = u2 = ul3 = 14 Hz: Not all the means are equal. SS df F ANOVA Source of Variation Between Groups Within Groups Total MS 2.2944 P-value 0.0003 Fcrit 6.2167 6.8832 3 15.8316 1.5942 11 0.1449 8.4773 14 The value of test statistics is: F=15.8316 P-value=0.0003 Conclusion: The p-value of F test is less than 0.01. Hence we reject null hypothesis and conclude that the true mean wages differ for the four occupations. b) Assumptions required for one way ANOVA: 1) The hourly wages of workers should be normally distributed. 2) The hourly wages of workers for four occupations have equal variances. 3) There should not be outliers in the data.