In the survey of 2255 US adults, we also learn that 970 of the respondents use the social networking site Facebook. Of the 970 Facebook users, the survey shows that on an average day:

• 15% update their status

• 22% comment on another's post or status

• 20% comment on another user's photo

• 26% “like” another user's content

• 10% send another user a private message

(a) For each of the bulleted activities, find a 95% confidence interval for the proportion of Facebook users engaging in that activity on an average day.

(b) Is it plausible that the proportion commenting on another's post or status is the same as the proportion updating their status? Justify your answer.

Approximately 10% of Americans are left-handed (we will treat this as a known population parameter). A study on the relationship between handedness and profession found that in a random sample of 105 lawyers, 16 of them were left-handed. Test the hypothesis that the proportion of left-handed lawyers differs from the proportion of left-handed Americans.

(a) Clearly state the null and alternative hypotheses.

(b) Calculate the test statistic and p-value.

(c) What do we conclude at the 5% significance level? At the 10% significance level?

In a recent study, 2006 randomly selected US adults (age 18 or older) were asked to give the number of people in the last six months “with whom you discussed matters that are important to you.” The average number of close confidants was 2.2, with a standard deviation of 1.4.

(a) Find the margin of error for this estimate if we want 95% confidence.

(b) Find and interpret a 95% confidence interval for average number of close confidants.