Question

(a) Suppose n = 6 and the sample correlation coefficient is r = 0.908. Is r significant at the 1% level of significance (based on a two-tailed test)? (Round your answers to three decimal places.) t = critical t =

(b) Suppose n = 10 and the sample correlation coefficient is r = 0.908. Is r significant at the 1% level of significance (based on a two-tailed test)? (Round your answers to three decimal places.) t = critical t =

Answer 1

a) Test statistic t = r * Sqrt (n -2)/sqrt[ 1- r​​​​​​2​​​​​]

t = 0.908 * sqrt ( 4) / sqrt [ 1 -0.9082]

t = 4.334

tCritical for a = 0.01 and d.f = n -2 = 4 , two tailed test

tCrit = t​​​​​​a/2, n-2 = t​​​​​​0.005,4 = 4.602

Here t = 4.334 , critical t = 4.602  

t < t critical , we fail to reject Ho , r is not significant

b)

Now for r = 0.908 , n = 10

t = 0.908*Sqrt (8)/ Sqrt [ 1 - 0.9082]

t = 6.130

tCritical for a = 0.01 , d.f = n -2 = 8

critical t = t​​​​​​0.005 , 8  = 3.355

t = 6.130 and critical t = 3.335

t > t critical , we reject null hypothesis , r is significant