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- r2]

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 = ta/2, n-2 = t0.005,4 = 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 = t0.005 , 8 = 3.355

t = 6.130 and critical t = 3.335

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

(a) Suppose n = 6 and the sample correlation
coefficient is r = 0.894. 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
=
Conclusion:
Yes, the correlation coefficient ρ is significantly
different from 0 at the 0.01 level of significance.
No, the correlation coefficient ρ is not significantly
different from 0 at the 0.01 level of
significance.
(b) Suppose n = 10 and...

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