Select all of the following choices that are possible confidence intervals on the population value of Pearson's correlation:
true
true
(-0.4, 0.6)
true
(0.3, 0.5)
true
(-0.85, -0.47)
false
(0.72, 1.2)
All of them are possible except for (0.72, 1.2). The population correlation cannot be above 1.
A sample of 28 was taken from a population, and r = .45. What is the 95% confidence interval for the population correlation?
true
false
(.058, .842)
false
(.093, .877)
false
(.058, .687)
true
(.093, .705)
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 sample correlation is -0.8. If the sample size was 40, then the 99% confidence interval states that the population correlation lies between -.909 and
-.589
0.002
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.