Question

A poll conducted in 2013 found that the proportion of of U.S. adult Twitter users who get at least some news on Twitter was 0.52. The standard error for this estimate was 0.024, and a normal distribution may be used to model the sample proportion.

1. Construct a 99% confidence interval for the proportion of U.S. adult Twitter users who got some news on Twitter. Round to four decimal places.

to

2. Identify each of the following statements as true or false.

  ?    True    False      1. We can be 99% confident that the true percentage of U.S. adults Twitter users who get some news through Twitter is between the upper and lower bounds of the confidence interval.

  ?    True    False      2. If we want to reduce the standard error of the estimate, we should collect less data.

  ?    True    False      3. If we construct a 90% confidence interval for the percentage of U.S. adults Twitter users who get some news through Twitter, this confidence interval will be narrower than a corresponding 99% confidence interval.

  ?    True    False      4. Since the standard error is 2.4%, we can conclude that 97.6% of all U.S. adult Twitter users were included in the study.

Answer 1

pcap = 0.52
SE = 0.024

#1.
z-value = 2.58

CI = (pcap - z*SE, pcap + z*SE)
CI = (0.52 - 2.58 * 0.024 , 0.52 + 2.58 * 0.024)
CI = (0.4581, 0.5819)

#2.
True

false

true

false