chapter 1

Chapter 7: Statistical Intervals Based on a Single Sample20. Because the sample size is so large, the simpler formula (7.11) for the confidence interval forp is sufficient.(.15)(.85). 15 ± 2.58 = .15±.013 =4722(.137,.163)13321. p ˆ = = . 2468539.2468 +2( 1.645)2( 539); the 95% lower confidence bound is:−1.6451 +(.2468)(.7532) ( 1.645)+539 4( 539)2( 1.645)53922.2493 − .0307=1.005= .21822. p ˆ = . 072 ; the 99% upper confidence bound is:.072 +2( 2.33)2( 487)+ 2.331 +2(.072)(.928) ( 2.33)+2487 4( 487)2( 2.33)487.0776 + .0279== .10431.011123.24a. p ˆ = = . 648637.6486 +( 2.58)2( 37)2; The 99% confidence interval for p is± 2.581 +2(.6486)(.3514) ( 2.58)+237 4( 37)2( 2.58)37.7386 ± .2216==1.1799(.438,.814)b.224( 2.58) (.25) − ( 2.58) (.01) ± 4( 2.58) (.25)(.25− .01) + .01( 2.58)2n =.013.261636 ± 3.3282=≈ 659.01424. n = 56, x = 8. 17 , s = 1.42; For a 95% C.I., z = 1. 96⎛1.42⎞8 .17 1.96⎜⎟ =⎝ 56 ⎠( 7.798,8.542)224α2. The interval is± . We make no assumptions about the distribution ifpercentage elongation.