Question

Constructing Confidence Intervals. In Exercises 21-24, use the sample data and confi- dence level to construct the confidence interval estimate of the population proportion p. 21. n = 500, x = 200, 95% confidence 22. n = 1200, x = 800, 99% confidence 23. n = 1068, x = 267,98% confidence

Answer 1

21) Solution: The provided information iſ as follows: Sample size AESOO number of fawoable cases confidence level O 0.95 XE o.os 0.4 Sample proportionat 200 Sd za zici. = The critical value for gao.o5 is ligo The coresponding confidence interiel is Computed shown below ст ſ- étze z. CAR (فرش (0:4–19 4-1.96/0.4(1-0.4) 0.4+1-96 10.4 Sou 60.4(1-04) 500 C0.4-0.043 0.44 0.043) CI = (0.357,-0.443) Therefore the 95% confidence internal is CI= (0.357, 0,443)

223 në 200 Solution The provided information is as fellows's Sample size number of favorable cases X = 800 Sample proportion pats doo 0.667 200 confidence level IQ = 0,99 a = 0.01 The critical value for x=0.01 is 2227922= 2 - 576. The conespording confidence interval is computed as shown below.. CI=(-2. BC-2 $12516 Chen n =(0662 - 2-5760.667(1-0,667) 200 0.667 + 2.576 0.667 C1-0.667) 200 0.667 – 0.035, 0.667 +0.035) Co. 632, 0.702) CI Therefore the 99% confidence internal is SI = (0-632,0.702)

23) Solution: _The provided in formation iſ as folloes's Sample size ni 1068 Aumbex of favorables cases X= 267 Sample pooportion p= X. 267. 3 267 0.25 1068 n confidence level l- ao.98 x = 0.02 The critical value for XE 0.02 iš 2 321-642 2.326 The Corresponding confidence in temel is computed as follows CI=/- 2c (1-2) (5-82 Ôt zq 48-7 = (0.25=2:326 = (0,25- 2:326 10.25(1-0,25) 1068 0.25 +2.326 0.25(1-0.25) 1068 = (0-25 31 0,25+ 0.031 CI= (0.219, 0.2812 Therefore the 98% confidence internalis (0.219,0.2812