Social Media
A survey showed that when a sample group was asked whether they used Facebook for networking, staying connected, or playing games, about 80% said they used it for staying connected.
a. Assuming the sample size was 5000, how many in the sample said they were using it to stay connected?
b. Is the sample size large enough to apply the Central Limit Theorem? Explain. Assume the other conditions are met.
c. Find a 95% confidence interval for the proportion that said they were using it to stay connected.
d. Find the width of the interval you found in part c by subtracting the lower limit from the upper limit. Round your answer to the nearest whole percentage.
e. Now assume the sample size was 20,000. How many would have said they were using it stay connected?
f. Find a 95% confidence interval for the population that said they were using it to stay connected using the numbers from part e.
g. What is the width of the interval you found in part f?
h. When the sample size is multiplied by 4 (as it was here, going from 5000 to 20,000), is the interval width decreased by a factor of 4? In other words, is the interval for the larger sample size one-fourth (1/4) of the interval for the smaller sample size? If not, what is it divided by?