Problem 1 A random sample of size 16 results in mean of 5 and standard deviation of 2. a) Test the hypothesis that the population mean is equal to 4 versus the hypothesis that it is not equal to 4 at or = .01. b) Test the hypothesis that that the population mean is equal to 4 versus the hypothesis that it is greater than 4 at a =.05 .Problem 2 From a random sample of 100 objects, 20 of them have orange color. The proportion of orange objects is the main research question. a) Is this a small or large sample for the purposes of testing for population proportion? Explain. b) Test the hypothesis at a=.1 that the population proportion of green objects is less than 0.3.c) Define "Type I error" in general d) Define "Type II error" in general e) What is the interpretation of a p-value