Statistics
1. We would like to estimate the average amount of time that an undergraduate business student studies outside of class each week for the business statistics course. A random sample of 100 is selected. The sample mean is 2.2 hours and the s2 = 2.25 hours. How large sample would be needed if we wanted to estimate the true mean with a maximum error of estimation of 15 minutes with 95% confidence?
Hello again, Farrah. Your notation is a little confusing, so I'll give you the answers in a couple of different ways. You say that the sample mean is 2.2 hours, with s2 = 2.25 hours. That could be s^2 (sample variance), but then the units would have to be hours^2, not hours. (The ^ indicates exponentiation -- also written **). So, you want the radius of the confidence interval to be 15 minutes, or 0.25 hours. A 95% confidence interval has a radius of 1.96 standard deviations, so you want s = 0.125. Now the standard error of the mean is equal to the standard deviation divided by the square root of n. So if you mean that s^2 = 2.25 hours^2, then s = 1.5 hours, and you would need a sample size of (s*1.96/0.25)^2 = 139. If you mean that s = 2.25 hours, then you would need 312.