Looking for Help- Estimate a Population Meam

Question

Assume that a sample is used to estimate a population mean . Find the 99.5% confidence interval for a sample of size 40 with a mean of 24.7 and a standard deviation of 21.8. Enter your answer accurate to one decimal place.I am 99.5% confident that the mean  is between ________and _______

Answer 1

First, we must determine whether to use Z or t. As we only have the sample standard deviation to work with and no distribution information about the population, we should use t with n-1 degrees of freedom, which is 40-1 = 39.

Also, I am going to assume that the standard deviation provided is that of the sample and not an estimate of the population standard deviation, based on how the item is worded.

The formula for finding the confidence interval limits is M ± t*SE, where M is the sample mean, t is the t-value associated with this confidence interval (two-tails, 99.5% confidence, 39 degrees of freedom), and SE is the (estimated) standard error of the sampling distribution.

M = 24.7 (given)

t = 2.96 (use whatever tools your instructor gave you to find this; I used the t.inv.2t function in Excel)

SE = SD/(n-1) = 21.8/√(40-1) = 3.49

24.7 ± 2.96*3.49 = 14.37, 35.03

Therefore, you are 99.5% confident that your true population mean is between 14.37 and 35.03.