In 2010, the online security firm Symantec estimated that 63% of computer users don’t change their passwords very often (cnet.com/news/survey-63-dont -change passwords-very-often, retrieved November 19, 2016). Suppose that you want to carry out a new survey to estimate the proportion of students at your school who do not change their password.

a. What is the required sample size if you want to estimate this proportion with a margin of error of 0.05? Calculate the required sample size first using 0.63 as a preliminary estimate of p and then using the conservative value of 0.5. How do the two sample sizes compare?

b. What sample size would you recommend? Justify your answer.