Question

Employers often use standardized measures to gauge how likely it is that a new employee with little to no experience will succeed in their company. One such factor is intelligence, measured using the Intelligence Quotient (IQ). To show that this factor is related to job success, an organizational psychologist measures the IQ score and job performance (in units sold per day) in a sample of 10 new employees.

IQ	Job Performance
100	16
115	35
108	32
98	19
120	47
147	54
132	48
85	52
105	23
110	36

(a) Convert the following data to ranks and then compute a Spearman correlation coefficient. (Round your answer to three decimal places.)
_____

(b) Using a two-tailed test at a 0.05 level of significance, state the decision to retain or reject the null hypothesis.

Retain the null hypothesis.

Reject the null hypothesis.    

Answer 1

(a)

We make a table

IQ	Job Performance	RankI	RankJ	d=RankI-RankJ	d2
100	16	8	10	-2	4
115	35	4	6	-2	4
108	32	6	7	-1	1
98	19	9	9	0	0
120	47	3	4	-1	1
147	54	1	1	0	0
132	48	2	3	-1	1
85	52	10	2	8	64
105	23	7	8	-1	1
110	36	5	5	0	0
Total	N/A	N/A	N/A	0	76

The number of observations (n)=10

Spearman's rank correlation coefficient is given by

(b)

Now we perform the correlation test.

The test statistic is given by

The test statistic follows t distribution with df 8

The p-value is obatined as 0.107907

As the p-value is more than 0.05, we fail to reject the null hypothesis i.e. the null hypothesis is retained at 5% level of significance.

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