Question

A random sample of 100 felony trials showed a sample mean waiting time between arrest and trial = 173 days with a population standard deviation of waiting times = 28 days. Find a 99% confidence interval for the population mean waiting time. Stats question, I'm really struggling here. Please help me!

Answer 1

Answer: 165.78 < μ < 180.22

Explanation: Confidence Interval of a mean is a method to estimate the true population mean, i.e., we can get an interval where the true mean exists.

A confidence interval is calculated as

x ±
`z(\sigma)/(√(n) )`

z is z-score for 99% confidence, which is: z = 2.58

Then, the estimate is

173 ±
`2.58(28)/(√(100) )`

173 ± 2.58*2.8

173 ± 7.224

lower limit: 173 - 7.224 = 165.78

upper limit: 173 + 7.224 = 180.22

The 99% confidence interval of the mean is between 165.78 and 180.22 and it means that the true mean of this population is between those numbers with 99% of confidence.