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 __

Answer 1

a)

x                    =				591
sample size		n                    =		657.0
sample proportion     p̂		x/n=		0.9000
std error       =Se		=√(p*(1-p)/n) =		0.0117
for 95 % CI value of z=				1.96
margin of error E=z*std error                            =				0.0229
lower confidence bound=sample proportion-margin of error				0.8771
Upper confidence bound=sample proportion+margin of error				0.9229

  95% confidence interval =(0.877 , 0.923)

b)

  95% confidence interval =(.634 , 0.706)

c)

95% confidence interval =(0.522 , 0.598)