Sure! Here is the previous response with all symbols turned into words:
A confidence interval is a range of values that is likely to contain the population mean with a certain level of confidence. The formula for a confidence interval for a population mean is given by: sample mean plus or minus critical value times (population standard deviation divided by the square root of sample size), where sample mean is the sample mean, critical value is the critical value for the desired level of confidence, population standard deviation is the population standard deviation and sample size is the sample size.
In this case, we are given a sample size of 766, a sample mean of 68.4 and a population standard deviation of 12.8. We are also asked to find the 99.5% confidence interval.
First, we need to find the critical value for a 99.5% confidence level. This can be done using a z-table or calculator. The critical value for a 99.5% confidence level is approximately 2.807.
Plugging these values into the formula gives us: 68.4 plus or minus 2.807 times (12.8 divided by the square root of 766) which is approximately equal to 68.4 plus or minus 1.289.
So, the 99.5% confidence interval for the population mean is 67.111 is less than population mean which is less than 69.689.