Question

Social media users and news: In 2019 a poll found that more than half (55%) of U.S. adults get news (often or sometimes) from social media and the standard error for this estimate was 2.0 percentage points. Identify each of the following statements as true or false.


(a) The data provide statistically significant evidence that more than half of U.S. adults get news through social media. Use a significant level of αα = 0.01.

• false
• true

(b) Since the standard error is 2.0%, we can conclude that 98% of all U.S. adults were included in the study.

• false
• true

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

• true
• false

(d) If we construct a 90% confident interval for the percentage of U.S. adults who get some news through social media, this confidence interval will be wider than a corresponding 99% confidence interval.

• true
• false

Answer 1

a)

true (since for 0.01 level critical value z =2.33 ; and here test statistic =(55-0.50)/2 > 2.33)

b)

False (this is error for proportion who gets news from social media

c)

False (we should collect more datA)

d)

False (lower confidence level will have smaller confidence interval)

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