Cambria Among all adult Indiana residents 84% arehig school graduates. Answer qu

Question

Cambria Among all adult Indiana residents 84% arehig school graduates. Answer questions 19-22 based on the 2 sampling distribution of p for random samples of n·500 Indiana adult residents. 3 19 What fraction of sample proportions fall under 0.82? 14 a 0.0994 15 b 0.1112 16 c 17 d 0.1601 18 19 20 The fraction of sample proportions obtained from samples of size n-500 that fall within ±0.04 (4 20 percentage points) from the population proportion is 221 a 0.9498 222 b 0.9685 2230.9854 224 d 0.9922 0.1334 226 21 The lower and upper ends of the interval which contains the middle 95% of all sample proportion obtained 227 from samples of size n = 950 are: P.- p-- 228 a 229 b 230 c 231 d 0.779 0.881 232 233 22 In the previous question, in order to obtain a margin of error of±0.02 (MOE = 0.02) for the middle interval 234 that contains the middle 95% of all sample proportions, the minimum sample is: n- 235 a 236 b 237 c 0.806 0.855 0.817 0863 0.788 0.872 1468 1401 1356 1291 238 d 239

Explanation / Answer

p=0.84 ; n=500

here std error of prportion =(p(1-p)/n)1/2 =0.0164

19) hence P(X<0.82)=P(Z<(0.82-0.84)/0.0164)=P(Z<-1.2199)=0.1112

option B

20)proportion =P(-0.4/0.0164<Z<-0.4/0.0164)=P(-2.4397<Z<2.4397)=0.9854

option C

21)std error ==(p(1-p)/n)1/2 =0.0119

for 95% CI ; z =1.96

hence 95% middle values =p -/+ z*std error =0.817 ; 0.863

option B

22)here p=0.84 ; margin of error E =0.02 ; for 95% CI ; z=1.96

hence sample size n=p(1-p)*(Z/E)2 =1291

option D

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