In Exercise 6.116 on page 386, we see that the average number of close confidants in a random sample of 2006 US adults is 2.2 with a standard deviation of 1.4. If we want to estimate the number of close confidants with a margin of error within ±0.05 and with 99% confidence, how large a sample is needed?

Exercise 6.116

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.