Use Table 10 of Appendix B to find the 95 interval for r whe

Use Table 10 of Appendix B to find the 95% interval for r when a sample of n = 25 results in r = 0.35. (Give your answers correct to two decimal places.)

Solution

Use Table 10 of Appendix B to find the 95% interval for r when a sample of n = 25 results in r = 0.35. (Give your answers correct to two decimal places.)

The sampling distribution of z\' is approximately normally distributed and has a standard error of

= 1/sqrt( n-3) = 0.2132

The Z for a 95% confidence interval (Z_.95) is 1.96

Z value for r=0.35 is 0.3654 ( from Table)

Lower limit = 0.3654 - (1.96)(0.2132) = -0.052

Upper limit = 0.3654 + (1.96)(0.2132) = 0.783

convert the endpoints of the interval back to r using

-0.052 ? ? ? 0.6544

95% CI = ( -0.05, 0.65)     ( two decimals)