A poll conducted in 2013 found that 52 of US adult Twitter u

A poll conducted in 2013 found that 52% of U.S. adult Twitter user get at least some news on Twitter, and the standard error for this estimate was 2.4%. Identify each of the following statements as true or false. Provide an explanation justify each of your answers.

a) the data provide statistically significant evidence that more than half U.S. adult twitter users get some news throught Twitter. Use a significance level of alpha = 0.01

b) 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.

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

d) If we construct a 90% confidence interval for the perventage of U.S. adults Twitter suers who get some news through Twitter, this confidene interval will be wider than a corresponding 99% confidence interval.

Solution

a)

a) the data provide statistically significant evidence that more than half U.S. adult twitter users get some news throught Twitter. Use a significance level of alpha = 0.01

False, as less than 0.50 is less than 1 standard error from 0.52, so that is insignificant. [FALSE]

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b) 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.

FALSE. Standard error is not related with the proportion of the sample to the population.

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

FALSE. We should collect more data, as the standard error is inversely proportional to the square root of n.

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d) If we construct a 90% confidence interval for the perventage of U.S. adults Twitter suers who get some news through Twitter, this confidene interval will be wider than a corresponding 99% confidence interval.

FALSE. A larger confidence level always has greater width, when everything else is the same.