Question

The test-retest method is one way of establishing the reliability of a test. The test is administered, and then, at a later date, the same test is re-administered to the same individuals. The correlation coefficient is computed between the two sets of scores. The following test scores were obtained in a test-retest situation. (Round your answers to two decimal places.)

First Score	75	87	60	75	98	80	68	84	47	72
Second Score	73	89	53	76	95	79	73	79	52	69

(a) Find r.


(b) Set a 95% confidence interval for ρ.

lower limit
upper limit

Answer 1

a)

correlation coefficient r=

Sxy/(√Sxx*Syy) =

0.96

b)

95% confidence interval for v(c1,c2)= (v-z/√(n-3) ; v+z/√(n+3))=

(1.202,2.684)

hence 95% confidence interval for ρ= ((e2c1-1)/(e2c1+1) ; (e2c2-1)/(e2c2+1)) =

(0.834,0.991)

lower limit =0.83

upper limit =0.99