Problem 6 [10 points = 3 + 7] Quality Control specialists design a study aimed at estimating the average assembly time for a new device. They assume that individual records are independent normally distributed with population standard deviation = = 2.5 minutes. Find the smallest sample size = n, such that the 95% confidence interval for the population mean = is no wider than 1 minute. 1. Show the critical value for design of this study 2. Indicate the formula used in this case and show the smallest sample size needed. Solution

Problem 7 [10 points = 3 + 7] Bureau of Labor Statistics experts design a study aimed at estimating the unknown proportion = p of self-employed programmers. They intend to use confidence level = C = 0.90 and want to have the margin of error bounded by B = 2%. Find the smallest sample size n that will be required for this study. 1. Show the critical value needed for the study 2. Indicate which formula you use in this case and show the smallest sample size needed. Solution