What is the lower and upper bound?

Question

A simple random sample of size n equals 350 individuals who are currently employed is asked if they work at home at least once per week. Of the 350 employed individuals​ surveyed, 28

responded that they did work at home at least once per week. Construct a​ 99% confidence interval for the population proportion of employed individuals who work at home at least once per week.

Answer 1

sample proportion (phat) = 28/350 = 0.08

sample size (n) = 350

z-critical value for 99% confidence interval is z-score corresponding to 99.5% probability (because 99% confidence interval is the middle 99% of area, leaving 0.5% at each tail) = 2.58

Confidence Interval = phat +/- z-critical * square root(phat * (1-phat)/n)

= 0.08 +/- 2.58 * square root (0.08*0.92/350)