Question

Are the types of professional jobs held in the computing industry independent of the number of years a person has worked in the industry? Suppose 243 workers are interviewed. Use the results obtained to determine whether type of professional job held in the computer industry is independent of years worked in the industry. Let = .01. Professional Position Years Manager Programmer Operator Systems Analyst 0–3 6 39 11 13 4–8 28 16 23 24 More than 8 42 10 12 19 Round the intermediate values to 2 decimal places. Round your answer to 2 decimal places, the tolerance is +/-0.05. Observed = Position is of number of years of experience.

Answer 1

here null hypothesis:Ho: type of professional job held in the computer industry is independent of years worked in the industry

alternate hypothesis: Ha: type of professional job held in the computer industry is dependent of years worked in the industry

degree of freedom =(row-1)*(column-1)=(4-1)*(3-1)=6

for 6 df and 0.01 level rejection region >16.812

applying chi squae test of independence:

Expected	Ei=Σrow*Σcolumn/Σtotal	0-3	4-8	>8	Total
	Manager	21.580	28.460	25.960	76
	Programmer	18.460	24.340	22.200	65
	operator	13.060	17.230	15.710	46
	system analyst	15.900	20.970	19.130	56
	Total	69	91	83	243
chi square    χ2	=(Oi-Ei)2/Ei	0-3	4-8	>8	Total
	Manager	11.250	0.010	9.910	21.170
	Programmer	22.850	2.860	6.700	32.410
	operator	0.320	1.930	0.880	3.130
	system analyst	0.530	0.440	0.000	0.970
	Total	34.950	5.240	17.490	57.680

chi square test statistic =57.68 ( please try 57.70 if this comes wrong)

as test statistic is in rejection region we reject null hypothesis ; we have sufficient evidence at 0.01 level to conclude that  type of professional job held in the computer industry is dependent of years worked in the industry.