chapter 1

Chapter 7: Statistical Intervals Based on a Single SampleSupplementary Exercises47.a. n = 48, x = 8. 079 , s 2 = 23.7017, and s = 4.868.A 95% C.I. for µ = the true average strength iss4.868x ± 1 .96 = 8.079 ± 1.96 = 8.079 ± 1.377 =n48( 6.702,9.456)13b. p ˆ = = . 2708481.96.2708+22( 48). A 95% C.I. is± 1.96(.2708)(.7292)1.961+482481.96+42( 48)2.3108 ± .1319==1.0800(.166,.410)48. A 98% t C.I. requires tn−= t 2. 896 . The interval isα / 2, 1 .01,8=7.2188 .0 2.896 = 188.0 ± 7.0 =9( 181.0,195.0)± .49.a. There appears to be a slight positive skew in the middle half of the sample, but the lowerwhisker is much longer than the upper whisker. The extent of variability is rathersubstantial, although there are no outliers.203040%porevolume50b. The pattern of points in a normal probability plot is reasonably linear, so, yes, normalityis plausible.c. n = 18, x = 38. 66 , s = 8.473, and t 2. 586. 01,17=8.47338 .66 2.586 = 38.66 ± 5.13 =18232. The 98% confidence interval is( 33.53,43.79)± .