Question

The Pew Research Center Internet Project conducted a survey of 857 Internet users. This survey provided a variety of statistics on them. If required, round your answers to four decimal places.

(a) The sample survey showed that 90% of respondents said the Internet has been a good thing for them personally. Develop a 95% confidence interval for the proportion of respondents who say the Internet has been a good thing for them personally. 0.880 to 0.920

(b) The sample survey showed that 67% of Internet users said the Internet has generally strengthened their relationship with family and friends. Develop a 95% confidence interval for the proportion of respondents who say the Internet has strengthened their relationship with family and friends. to

(c) Fifty-six percent of Internet users have seen an online group come together to help a person or community solve a problem, whereas only 25% have left an online group because of unpleasant interaction. Develop a 95% confidence interval for the proportion of Internet users who say online groups have helped solve a problem. to

(d) Compare the margin of error for the interval estimates in parts (a), (b), and (c). How is the margin of error related to the sample proportion? The margin of error as p gets closer to .50.

Answer 1

a)

sample size          n=		857
sample proportion p̂ =x/n=		0.9000
std error se= √(p*(1-p)/n) =		0.0102
for 95 % CI value of z=		1.960
margin of error E=z*std error   =		0.020
lower bound=p̂ -E                       =		0.8799
Upper bound=p̂ +E                     =		0.9201
from above 95% confidence interval for population proportion =(0.8799 ,0.9201)

b)

std error se= √(p*(1-p)/n) =		0.0161
for 95 % CI value of z=		1.960
margin of error E=z*std error   =		0.031
lower bound=p̂ -E                       =		0.6385
Upper bound=p̂ +E                     =		0.7015
from above 95% confidence interval for population proportion =(0.6385 ,0.7015)

c)

std error se= √(p*(1-p)/n) =		0.0170
for 95 % CI value of z=		1.960
margin of error E=z*std error   =		0.033
lower bound=p̂ -E                       =		0.5268
Upper bound=p̂ +E                     =		0.5932
from above 95% confidence interval for population proportion =(0.5268 , 0.5932)

d)

The margin of error increases as p gets closer to .50