Question

Employers often use standardized measures to gauge how likely it is that a new employee with little to no experien psychologist measures the IQ score and job performance (in units sold per day) in a sample of 10 new employees IQ Job Performance 100 115 108 98 120 147 132 85 105 110 15 36 17 46 56 47 54 29 35 (a) Convert the following data to ranks and then compute a Spearman correlation coefficient. (Round your a (b) Using a two-tailed test at a 0.05 level of significance, state the decision to retain or reject the null hypot O Retain the null hypothesis. O Reject the null hypothesis You may need to use the appropriate table in Appendix C to answer this question Additional Materials E eBook

Answer 1

a) The Spearman's Correlation coefficient is calculated by

_{Where N= No of samples}

_{D= Difference of Ranks of X and Y}

X values	Y values	X rank	Y rank	X(rank)-Y(rank)	D(Square of difference of ranks)
100	15	3	1	2	4
115	36	7	6	1	1
108	33	5	4	1	1
98	17	2	2	0	0
120	46	8	7	1	1
147	56	10	10	0	0
132	47	9	8	1	1
85	54	1	9	-8	64
105	29	4	3	1	1
110	35	6	5	1	1
				Sum of D=	74

Now, by formula

$r_{s}=1-\frac{6*\sum D}{N^{3}-N}=1-\frac{6*74}{1000-10}=0.552$

b) The p- value associated with the spearman's coefficient is

P-value (2-tailed) = 0.0984.

Since it is greater than 0.05 hence we fail to reject null hypothesis.