00:01
Here we have a random sample of size 40, which yielded a sample average of 142 .62 .62.
00:07
We are also told that the population standard deviation is 32 .99.
00:13
And so for part a, we were asked to find a point estimate for the population mean, and part b, a 90 % confidence interval for the population mean.
00:24
Now, given a sample, the best estimate, if all we have is the sample, the best estimate of the population mean is equal to the sample mean.
00:36
So in this situation that's 142 .62.
00:43
And for part b, since we actually have the population standard deviation, our confidence interval for the population mean is based on the standard normal distribution, and it's given by the point estimate for the mean plus or minus a confidence coefficient z subalpha over 2 times the population standard deviation divided by the square root of the sample size.
01:15
We want to find a 90 % confidence interval.
01:18
90 % confidence means that alpha is 1 minus .9 or .1...