Problems [due 28 Nov 2021 - group activity] 1. When a manufacturing process is operating properly, the mean length of a certain part is known to be 6.175 inches, and lengths are normally distributed. The standard deviation of this length is 0.0080 inches. If a sample consisting of 6 items taken from current production has a mean length of 6.168 inches, is there evidence at the 5% level of significance that some adjustment of the process is required? Given: mu, o, n, x, 5% level of significance Approach: compare z-values (test statistic z vs critical z1=-1.96); p-values (@ (-z1) and 1- (21) vs 5%); x values (critical x value vs *) Answer: some adjustment of the process is required 2. A cocoa packaging machine fills bags so that the bag contents have a standard deviation of 3.5 g. Weights of contents of bags are normally distributed. 6 a) If a random sample of 20 bags gives a mean of 102.0 g, what are the 99% confidence limits for the mean weight of the population (i.e., all bags)? Given: o, n, x, 99% confidence limits Approach: Find critical z1 value at 99% CL; Det. x values X = x - z1 (Ox) to X = x + z1 (Ox) b) What sample size (how many bags) would have to be taken so that a person would be 95% confident that the population mean was not smaller than the sample mean minus 1 g? Given: 95% CL, H >= x -1, n bags =? Approach: Find critical z1 value at 95% CL; set up test statistic equation/s to get n)