Question

A company applies an aptitude test to all those who apply for jobs as programmers. The results of these tests are analyzed according to their precedence (general advertising, ads in specialized magazines, employment agencies, personal recommendations or people who come spontaneously). With a significance level of 0.025, determine if there is a difference between the results of these tests according to their precedence. Your work should have detailed procedure, in this exercise you can use the tool offered by Excel for the required test, but you have to have the appropriate analysis.

General Pub	36	47	38	51	62	78	60	47	49	53	26	38	61	39	43
Rev Esp.	58	64	62	47	71	90	65	82	61	59
Ag Emp.	47	59	48	81	66	50	42	53
Rec Per.	67	61	82	97	65	72	54	59	58
Spontaneous	38	47	80	41	38	66	50

Answer 1

The hypotheses will be

H₀: all the precedence is equal .i.e. there is no significant difference between the precedence

H₁: At least two of the precedence is not equal i.e. there is a significant difference between the precedence

The appropriate analysis that can be used is ANOVA for a single factor. We can conduct this test using MS Excel.

Enter data → Data → Data Analysis → Anova: Single Factor

Provide the necessary details and make α=0.025 them the following appears.

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
General Pub.	15	728	48.53333	169.6952
Rev Esp.	10	659	65.9	152.9889
Ag Emp.	8	446	55.75	159.9286
Rec Per.	9	615	68.33333	186
Spontaneous	7	360	51.42857	253.2857

ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	3248.561	4	812.1401	4.53488	0.003736	3.093288
Within Groups	7879.848	44	179.0874
Total	11128.41	48

The critical value of F for (4, 44) d.f and α=0.025 level of significance is 3.093288.

Since the calculated value is greater than critical value and the p-value is less than 0.025, we reject the null hypothesis and conclude that with 97.5% confidence that the precedence differ significantly. So thers is a difference between the results of these tests according to their precedence.

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