00:01
For this question, we were asked how large a sample was necessary to estimate a population mean with precision of plus or minus 0 .006 inches at 90 % confidence.
00:14
That is, we want the population mean, and we know that the population has a standard deviation of 0 .04.
00:24
Population standard deviation is denoted sigma, and we're also told that the population is normally distributed.
00:30
We actually want to estimate the population mean length.
00:37
In the situation where we happen to know the population standard deviation confidence interval, so we take a sample from the population, we use that sample information to construct a confidence interval for the population mean, and it's calculated using the sample mean plus or minus some margin of error.
01:02
So it's this margin of error that we want to be no bigger than 0 .006.
01:13
When we happen to know the population standard deviation, the margin of error is calculated as a critical value, z sub alpha over 2, times the population standard deviation over the square root of the sample size...