Confidence Intervals for Correlation and Proportion
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Answers
All of them are possible except for (0.72, 1.2). The population correlation cannot be above 1.
The corresponding z' for r = .45 is .485. The standard error = 1/sqrt(28-3) = .20. The Z for a 95% confidence interval is 1.96. Thus, the upper limit of the confidence interval is .485 + (1.96)(.20). You get .877. The lower limit of the confidence interval is .485 - (1.96)(.20). You get .093. Convert back to r and you get (.093, .705).
The corresponding z' for r = -.8 is -1.099. The standard error = 1/sqrt(40-3) = .164. The Z for a 99% confidence interval is 2.58. Thus, the upper limit of the confidence interval is -1.099 + (2.58)(.164). You get -.676. Convert back to r and you get -.589.