Question

6.24 In a survey of 2255 randomly selected US adults (age 18 or older), 1787 of them use the Internet regularly. Of the Internet users, 1054 use a social networking site. Find and interpret a 95% confidence interval for each of the following proportions: a) Proportion of US adults who use the internet regularly. b) Proportion of US adult Internet users who use a social networking site. c) Proportion of all US adults who use a social networking site. Use the confidence interval to estimate whether it is plausible that 50% of all US adults use a social networking site.

Answer 1

Sot a Number ok uS adulla 2ampled, = 22S5 Number ot US aduit Nampled who we fhe 9alernd vegularly, x = Sample proportion t sti 22 S5 0.79246119 Signiticance level, 1-Contidence -O.9 Crihcal z-value tl 20.02s1-96 Sandard error = -7925) C1- o7925 2255 00085 396 Margin ot error, E 2 - CI-94) (o-oo 85394) O.O1623753 O.0167 95%. COntidence 9nlerval n given by C PE Lower limit = o.7925-0.O167 o-7425 +0 O167 0.8092 pper limit E (O.775e, 0. B092) So, 45 Contdence In1e,val

Sample number 0f Salernet Usera, n 1784 Sample Numbec of Jalernet social networkig UACYA who use 入re, ×= 1o5y Sample proportor, = 1o54 OM898IS33 七8七」 3685 0 Signitcance level, 1- Contidence 1-0.95: o.OS CriGcal zvalue = 1-94 OO25 Tandard Eror Co.0848) 01-05 998) O.O13$57 tst Margin of errov CE) K Sondand EVYOY - .a0) Co.01c9 2OO22S OONN844 interval 95% Contidence Sven by pE O.S818 0.0228 lower imit PO6126 tan Upper imit= p+E = 0.5098 o.O 228 9 a dult Contidence inlerval tor pro portion ot 9nternet 95' Social netorking i n(0-56 ,o.126) who use a

Sample nuomber ot UnCYA, n 2255 Sample numbev of inlernet CYA natworking who une a houal net Sample proportion, p O.4474OS7 2255 o4674 8 Signiticanre level, o contidence 1-O.95 = 0.O5 1-96 Crikcal z-value 6.46749 C-0.4674) 3landard CYYor 1P 2.255 FOOl0Mo 68 2o.o10S Slandard Margn of crror, E = o.6206 9) C0.0105) O02058 P- E lower Gmit= 4674- 0.0206 0.4468 P+E = 0.464 + 0.0206 O.488 Cpper mit = US adult 95 Contidence inlerval tur pro portion ot al The Ao cial networking ite Se a (O.4468, 0.48&) who to eaimate hat So ot all us adult It h not plausible Social netu ovlking Aie T becaune the now ne a don not Contidence nerval in pavt