4.10 Twitter users and news, Part II. A poll conducted in 2013 found that 52% of

Question

4.10 Twitter users and news, Part II. A poll conducted in 2013 found that 52% of U.S adult Twitter users 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 to justify each of your answers. (a) The data provide statistically significant evidence that more than half of U.S. adult Twitter users get some news through Twitter. Use a significance level of -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 the estimate, we should collect less data (d) If we construct a 90% confidence interval for the percentage of U.S. adults Twitter users who be wider than a corresponding get some news through Twitter, this confidence interval w 99% confidence interval

Explanation / Answer

Ans:

a)

H0:p=0.5

Ha:p>0.5

z=(0.52-0.5)/0.024=0.83

p-value=P(z>0.83)=0.2033

As,p-value>0.01,we reject null hypothesis.

There is significant evidence that mor than half of the US adults twitter users get some news through twitter.

Hence,above statement is true.

b)fasle

c)False,as standard error decreases when we increase the sample size.

d)False,as we increase the confidence level,Confidence interval becomes wider.

So,99% CI will be wider than 90% CI.

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