homework_4 - 2028 Basic Statistical Methods Homework 4 This homework is due Thursday October 6th in class BEFORE class starts Late papers will not be

2028: Basic Statistical Methods Homework 4 This homework is due Thursday, October 6th in class BEFORE class starts . Late papers will not be accepted. Please do not turn in any papers to any mailbox. • Please remember to staple if you turn in more than one page. • You must SHOW ALL WORK. If you do not show your work, you may not receive full credit. I Mean Confidence Interval Estimation 1 A sample of 61 bottles of chemical solution is obtained and the solution densities are measured. The sample mean is ¯ x = 0 . 768 and the sample standard deviation is s = 0 . 0231. Find the value c for which μ ∈ ( c, ∞ ) is a one-sided 99% t-interval for the average solution density μ . Is it plausible that the average solution density is less than 0.765? 2 Textbook 8-88 page 279 II Proportion Parameter Estimation 1 A stamping machine produces can tops. Randomly selected can top produced by this machine is non-conforming with probability 0.003. i. What is the exact theoretical distribution for the number of non-confirming items in a batch of n items. What assumptions about the production process should be made so that this distributional assumption is valid.