Question

An electronic company in the recruitment of employees, conducts two stages of selection, namely the interview stage and psychological testing. But because the cost of psychological testing is increasingly expensive, the company plans to cancel the psychological testing process if the results of the interview are good enough. For this reason, the company assumes a positive correlation between interviews and psychological tests. This means that workers who are hired usually have high scores on interview tests and psychological tests. For this reason, human resource managers are instructed to test whether the hypothesis is correct. Therefore, the Human Resources Manager took interviews and psychological tests from 35 applicants. Help these human resource managers by using the Spearman Correlation Test with an error rate of 0.01 !

Job Applicant	Score on Interview test	Score on psychological test
1	81	113
2	88	88
3	55	76
4	83	129
5	78	99
6	93	142
7	65	93
8	87	136
9	95	82
10	76	91
11	60	83
12	85	96
13	93	126
14	66	108
15	90	95
16	69	65
17	87	96
18	68	101
19	81	111
20	84	121
21	82	83
22	90	79
23	63	71
24	78	108
25	73	68
26	79	121
27	72	109
28	95	121
29	81	140
30	87	132
31	93	135
32	85	143
33	91	118
34	94	147
35	94	138

Answer 1

Here we want to test  the company's claim that there is  a positive correlation between interviews and psychological tests.

The score on interview test and the score on psychological tests of 35 applicants is given

Let xi's be the score on interview test and yi's be the score on psychological test

Job Applicant	Score on an Interview test	Score on a psychological test
1	81	113
2	88	88
3	55	76
4	83	129
5	78	99
6	93	142
7	65	93
8	87	136
9	95	82
10	76	91
11	60	83
12	85	96
13	93	126
14	66	108
15	90	95
16	69	65
17	87	96
18	68	101
19	81	111
20	84	121
21	82	83
22	90	79
23	63	71
24	78	108
25	73	68
26	79	121
27	72	109
28	95	121
29	81	140
30	87	132
31	93	135
32	85	143
33	91	118
34	94	147
35	94	138

Now obtaining the correlation coefficient between interviews and psychological tests.(r)

Obtaining , and  

	x	y
1	81	113	-0.171428571	5.457143	0.029388	29.78041	-0.93551
2	88	88	6.828571429	-19.5429	46.62939	381.9233	-133.45
3	55	76	-26.17142857	-31.5429	684.9437	994.9518	825.5216
4	83	129	1.828571429	21.45714	3.343673	460.409	39.23592
5	78	99	-3.171428571	-8.54286	10.05796	72.98041	27.09306
6	93	142	11.82857143	34.45714	139.9151	1187.295	407.5788
7	65	93	-16.17142857	-14.5429	261.5151	211.4947	235.1788
8	87	136	5.828571429	28.45714	33.97224	809.809	165.8645
9	95	82	13.82857143	-25.5429	191.2294	652.4376	-353.221
10	76	91	-5.171428571	-16.5429	26.74367	273.6661	85.5502
11	60	83	-21.17142857	-24.5429	448.2294	602.3518	519.6073
12	85	96	3.828571429	-11.5429	14.65796	133.2376	-44.1927
13	93	126	11.82857143	18.45714	139.9151	340.6661	218.3216
14	66	108	-15.17142857	0.457143	230.1722	0.20898	-6.93551
15	90	95	8.828571429	-12.5429	77.94367	157.3233	-110.736
16	69	65	-12.17142857	-42.5429	148.1437	1809.895	517.8073
17	87	96	5.828571429	-11.5429	33.97224	133.2376	-67.2784
18	68	101	-13.17142857	-6.54286	173.4865	42.80898	86.17878
19	81	111	-0.171428571	3.457143	0.029388	11.95184	-0.59265
20	84	121	2.828571429	13.45714	8.000816	181.0947	38.06449
21	82	83	0.828571429	-24.5429	0.686531	602.3518	-20.3355
22	90	79	8.828571429	-28.5429	77.94367	814.6947	-251.993
23	63	71	-18.17142857	-36.5429	330.2008	1335.38	664.0359
24	78	108	-3.171428571	0.457143	10.05796	0.20898	-1.4498
25	73	68	-8.171428571	-39.5429	66.77224	1563.638	323.1216
26	79	121	-2.171428571	13.45714	4.715102	181.0947	-29.2212
27	72	109	-9.171428571	1.457143	84.1151	2.123265	-13.3641
28	95	121	13.82857143	13.45714	191.2294	181.0947	186.0931
29	81	140	-0.171428571	32.45714	0.029388	1053.466	-5.56408
30	87	132	5.828571429	24.45714	33.97224	598.1518	142.5502
31	93	135	11.82857143	27.45714	139.9151	753.8947	324.7788
32	85	143	3.828571429	35.45714	14.65796	1257.209	135.7502
33	91	118	9.828571429	10.45714	96.60082	109.3518	102.7788
34	94	147	12.82857143	39.45714	164.5722	1556.866	506.1788
35	94	138	12.82857143	30.45714	164.5722	927.6376	390.7216
Total	2841	3764	-2.27374E-13	-5.7E-14	4052.971	19424.69	4902.743
Mean	81.171429	107.5428571

From the calculation

= 81.171429

= 107.5428571

= 4052.971

, = 19424.69

and   = 4902.743

The correlation coefficient is given as (Spearman correlation formula)

= 0.552554785

Rounding off

r= 0.5526

Now for testing the significance of correlation coefficient

Let be the population correlation coefficient.

Hence the null hypothesis is given as

There is not signifiant correlation

There is not signifiant positive correlation

The test statistic is given is

= 0.5526 /0.1450844
=   3.808817

Rounding off

= 3.809

t = 0.08017

Obtaining the critical value with

df = n-2

= 33

From one tailed t -table

Dicision rule :

Reject the null hypothesis if t (calculated) > t(critical value)

Since    t (calculated) = 3.809 >   t(critical value) = 2.4448

We reject the null hypothesis.

Hence there is sufficient evidence to conclude that there is significant positive correlation

(

Verifying using R-output

)