Question 184106
Doane−Seward: Applied Statistics in Business and Economics, ch. 12:
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For each sample, do a test for zero correlation. 
(a) Use Appendix D to find the critical value of tα. 
(b) State the hypotheses about ρ. 
(c) Perform the t test and report your decision. 
(d) Find the critical value of rα and use it to perform the same hypothesis test.
a. r = +.45, n = 20, α = .05, two-tailed test
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a.
critical value for df = n-2 = 18 is r = 2.101
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b.State the hypotheses about ρ.
Ho: rho = 0
Ha: no it isn't
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c.Perform the t test and report your decision.
t = rsqrt[(n-2)/(1-r^2) = 0.45sqrt[18/(1-0.2025)] = 2.1379
Reject Ho because 2.1379 is greater than 2.101
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d.Find the critical value of rα and use it to perform the same hypothesis test.
r(alpha) = t(alpha)/sqrt(t^2(alpha) + n -2)
r(alpha) = 2.101/sqrt(2.101^2+20-2) = 2.101/4.73436 = 0.44378
Since r(alpha) is less that alpha=5%, reject Ho.
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Note: I'll leave the others to you.  Follow the example I have
given you.  Your text has these two test procedures on pages 
492 and 493
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Cheers,
Stan H.










b. r = −.35, n = 30, α = .10, two-tailed test
c. r = +.60, n = 7, α = .05, one-tailed test
d. r = −.30, n = 61, α = .01, one-tailed test