Question

The Pew Research Center Internet Project conducted a survey of 657 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.
	______ to _____
(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 (increases/decreases) as p gets closer to. 50

Answer 1

a)

sample success x =		2812
sample size          n=		3124
sample proportion p̂ =x/n=		0.9000
std error se= √(p*(1-p)/n) =		0.0054
for 95 % CI value of z=		1.960
margin of error E=z*std error   =		0.0105
lower bound=p̂ -E                       =		0.8895
Upper bound=p̂ +E                     =		0.9105
from above 95% confidence interval for population proportion =(0.8895 to 0.9105)

b)

95% confidence interval for population proportion =(0.6535 to 0.6865)

c)

95% confidence interval for population proportion =(0.2348 to 0.2652)

d)

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