Question

p a tclet ponts u that sume com ames have slailed lu teature emae models W าย ane nul et tradittr 1 nel tun wumen who hľalve tao l bilboards ld m at a ne tuvers tur the as1 2 .25 ars hese new mo ets called real people a still alhletic an d represent wt snakeswar an calls Ahat ts ear as ต osed to hat IS d The artrle ako re arts nn刁surve at 50ต women in which 87% a the respo dents said they were sattsted wth what te se in the mimar A car any's managers would Ike to us伫these data 1n de elap貣959 cmt ence. Interval estiman for the truc proportion of all women wno are satencd with 1hcir bodies Develop and interpret thc 35% confidence interval cstiman The cntdence nterval estimate匹| | p ; Rcund to Ihree decimal places as leeded.) Interpret the confndence interval estimate ○ A. With 95% confidence, the true proportion of all women who arn sateinen with their h des s within the interval found In para О в. with 9t5% cortdence, the sample praportion at al wamen who are satisted wth ther badies is equal 'n the true praportin c. w h 9 % conlidence u ue rupu'iun of all wormen who are sa slied willi lthe" budes s wiltım 3 małyms ol e"or of lhe samp Win 95% confidence, the sample propon on oral women who are satisfied ₩ith their bodies is within the nerval lound in part a. proportion ○ D.

Answer 1

Solution :

n =1500

$\hat p$ = 87% = 0.87

1 -$\hat p$ = 1 - 0.87 = 0.13

At 90% confidence level the z is ,

$\alpha$ = 1 - 90% = 1 - 0.90 = 0.10

$\alpha$ / 2 = 0.10 / 2 = 0.05

Z_$\alpha$/2 = Z_0.05 = 1.645

Margin of error = E = Z_{$\alpha$ / 2} * $\sqrt$(($\hat p$ * (1 - $\hat p$)) / n)

= 1.645 * ($\sqrt$((0.87 * 0.13) /1500)

= 0.024

A 90 % confidence interval for population proportion p is ,

$\hat p$- E < P <$\hat p$ + E

0.87 - 0.014 < p < 0.87 + 0.014

0.856< p < 0.901

Option A ) is correct.