The Pew Research Center Internet Project conducted a survey of 807 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. 0.8793 to 0.9207 (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. 0.6376 to 0.7024 (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. 0.577 to 0.5932

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
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Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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The Pew Research Center Internet Project conducted a survey of 807 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.
0.8793
to 0.9207
(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.
0.6376
to 0.7024
(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.
0.577
to 0.5932
(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
as p gets closer to .50.
Transcribed Image Text:The Pew Research Center Internet Project conducted a survey of 807 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. 0.8793 to 0.9207 (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. 0.6376 to 0.7024 (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. 0.577 to 0.5932 (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 as p gets closer to .50.
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