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 three decimal places.

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

1. 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.

2. Based on the interval, it is reasonable to believe that at least half of U.S. adult Twitter users get some news through Twitter.

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.

4. If we want to reduce the standard error of the estimate, we should collect less data.

Answer 1

1) At 99% confidence interval the critical value is z_0.005 = 2.58

The 99% confidence interval for population proportion is

+/- z_0.005 * SE

= 0.52 +/- 2.58 * 0.024

= 0.52 +/- 0.062

= 0.458, 0.582

2) 1 - False

    2 - True . Because 0.5 lies in the confidence interval.

    3 - True . Because by decreasing the confidence level, the margin of error also decreases and the width of the confidence interval becomes narrower.

   4 - False. Because to reduce the standard error , we should collect more data. Since by increasing the sample size, the standard error decreases.