Facebook Pew Research conducts polls on social media use. In 2012, 66 % of those surveyed reported using Facebook. In 2018, 76 % reported using Facebook. a. Assume that both polls used samples of 100 people. Do a test to see whether the proportion of people who reported using Facebook was significantly different in 2012 and 2018 using a 0.01 significance level. b. Repeat the problem, now assuming the sample sizes were both 1500. (The actual survey size in 2018 was 1785.) c. Comment on the effect of different sample sizes on the p-value and on the conclusion.
Facebook Pew Research conducts polls on social media use. In 2012, 66 % of those surveyed reported using Facebook. In 2018, 76 % reported using Facebook. a. Assume that both polls used samples of 100 people. Do a test to see whether the proportion of people who reported using Facebook was significantly different in 2012 and 2018 using a 0.01 significance level. b. Repeat the problem, now assuming the sample sizes were both 1500. (The actual survey size in 2018 was 1785.) c. Comment on the effect of different sample sizes on the p-value and on the conclusion.
Solution Summary: The author explains how to determine whether the proportion of people who reported using Facebook was significantly different in 2012 and 2018 at 0.01 significance level.
Facebook Pew Research conducts polls on social media use. In 2012,
66
%
of those surveyed reported using Facebook. In 2018,
76
%
reported using Facebook.
a. Assume that both polls used samples of 100 people. Do a test to see whether the proportion of people who reported using Facebook was significantly different in 2012 and 2018 using a
0.01
significance level.
b. Repeat the problem, now assuming the sample sizes were both 1500. (The actual survey size in 2018 was 1785.)
c. Comment on the effect of different sample sizes on the p-value and on the conclusion.
Definition Definition Number of subjects or observations included in a study. A large sample size typically provides more reliable results and better representation of the population. As sample size and width of confidence interval are inversely related, if the sample size is increased, the width of the confidence interval decreases.
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Part (b)
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Chapter 8 Solutions
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