Interval estimate when population standard deviation is known In a sample of n = 16, the mean is x = 80 kilograms. Also, you somehow know population standard deviation, o = 14. Give an estimate of the population mean at a 90% confidence level. (a) Obtain the standard error of the sample mean, SEM. The population is practically infinite, so you do not need the finite population correction factor. (b) From your confidence level, find the probability of committing a false positive, a. (c) Use quantile function ("=norminv()" in Excel) to find the z score that produces the CDF of a/2 and the z score that produces the CDF of 1 - a/2. Illustrate what you found with a sketch of the bell curve. Specifically, show the area containing your confidence level and the areas that contain a. Also indicate the z scores that are the boundaries of your confidence interval. (d) Convert the z scores from (c) to kilograms and state your final estimate of the population mean