Social networking sites such as Facebook and Twitter have become fixtures in the social lives of...
Social networking sites such as Facebook and Twitter have become fixtures in the social lives of many
people around the world. As a result, there’s been a growing interest in the impact that they have on our
daily lives and relationships.
A recent Pew Research poll surveyed U.S. residents to ask about their use of social media. Of the 156
respondents aged 18 to 22 who use Facebook, 30.7% stated that they updated their Facebook status at
least once per day.
Use the information above to answer the following questions.
1. Is .307 a parameter or a statistic? Explain.
2. Does this finding necessarily prove that 30.7% of all aged 18 to 22 year olds update their
Facebook status at least once per day?
Suppose we assume that our sample statistic, .307, is an unbiased estimator of our population
proportion, p. So, approximates the value of, If this is true, then we define the STANDARD ERROR of the sample statistic, , as
STANDARD ERROR= SE =
3. Compute the standard error of our sample statistic, =0.307. Show work.
4. Now, to go two standard errors on either side of , double the standard error, and then add the
result to and subtract the result from to form a reasonable interval estimate of p. Write your interval estimate below. Show work.
5. Do you know for certain if p, the overall proportion of U.S. adults aged 18 to 22 who update their
Facebook status at least one time per day, is contained in the interval?
6. Repeat number 4, if the sample statistic would have been 0.34. Write all supporting calculations
below (SE, interval).
7. Do we know for sure if p is contained in this interval?
In both cases, you have computed a 95% confidence interval for the proportion, p.
(95% confidence corresponds to roughly 2 standard error measurements).
9. Why did the interval vary from question 4 to question 6?
10. Do we know which interval is a better approximation to p?
Remember, the population proportion, p, represents the proportion of ALL Facebook users (aged 18-22)
who update their status daily.
Homework Answers
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