Question

Are the types of positions held in the IT industry independent of how long individuals have worked in the industry? Researchers determine the position held and years in the industry for 246 individuals working in the IT industry. The data can be found in the excel file job. Run the appropriate tests and place the screen shot of your MiniTab or excel output below. Run all tests at the 5% significance level. When running a chi square test for association, you MUST check off “each cell’s contribution to Chi-Square” in MiniTab (this is found by selecting “statistics” when in the test dialog box). If using Excel you must complete these by hand within excel.When running a one-way or two-way ANOVA test, also perform a Fisher’s LSD comparison test for any significant factors, at the 5% significance level. Experience Manager Programmer Operator System Analyst 0-3 6 37 10 13 4-8 25 16 26 24 More than 8 47 10 12 20

Answer 1

Χ2 test of independence:

Ho: Positions held in the IT industry are independent of how long individuals have worked in the industry

Ha: Positions held in the IT industry are dependent on how long individuals have worked in the industry

Experience	Manager	Programmer	Operator	System Analyst	Total
0 - 3	6	37	10	13	66
4 - 8	25	16	26	24	91
> 8	47	10	12	20	89
Total	78	63	48	57	246

Note: To get expected value for a cell, the formula is (row total * column total)/grand total. For example, for the cell "0 - 3 and Manager", the expected value will be (66 * 78)/246 = 20.93. Similarly for all the other cells

Chi-square Contingency Table Test for Independence
			Manager	Programmer	Operator	System Analyst	Total
	0 - 3	Observed	6	37	10	13	66
		Expected	20.93	16.90	12.88	15.29	66.00
		O - E	-14.93	20.10	-2.88	-2.29	0.00
		(O - E)² / E	10.65	23.90	0.64	0.34	35.53
	4 - 8	Observed	25	16	26	24	91
		Expected	28.85	23.30	17.76	21.09	91.00
		O - E	-3.85	-7.30	8.24	2.91	0.00
		(O - E)² / E	0.51	2.29	3.83	0.40	7.03
	> 8	Observed	47	10	12	20	89
		Expected	28.22	22.79	17.37	20.62	89.00
		O - E	18.78	-12.79	-5.37	-0.62	0.00
		(O - E)² / E	12.50	7.18	1.66	0.02	21.36
	Total	Observed	78	63	48	57	246
		Expected	78.00	63.00	48.00	57.00	246.00
		O - E	0.00	0.00	0.00	0.00	0.00
		(O - E)² / E	23.66	33.37	6.13	0.77	63.92
			63.92	chi-square
			6	df
			7.16E-12	p-value

Since the p- value < 0.05, we reject Ho

Conclusion: There is sufficient evidence that positions held in the IT industry are dependent on how long individuals have worked in the industry.