Question

The Pew Research Center Internet Project conducted a survey of 757 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 as p gets closer to .50.

Answer 1

n= 757

a) 95% confidence interval is

p= 0.9 and n= 757 and Z(critical)= 1.96

is 95% confidence interval for the proportion of respondents who say the Internet has been a good thing for them personally.

b) p=67%= 0.67 n= 757

is a 95% confidence interval for the proportion of respondents who say the Internet has strengthened their relationship with family and friends.

c) p= 56%= 0.56

is a 95% confidence interval for the proportion of Internet users who say online groups have helped solve a problem.

d) Greater the proportion value smaller the margin of error.