Lab 11 In this lab we will perform testing of hypotheses related to the population mean. This material is in Section 13.2. Three national bottling companies distribute cans of soft drinks labeled as containing 16 oz. We take the view that, to save money, they may put slightly less in each can, on average, so we'll test H0 : = 16 vs. Ha : < 16, where denotes the mean fill, using = 0.05. Let us assume that in fact company A fills at 16 oz, but that B and C consistently put in a bit less: suppose their three respective mean fills are A = 16 oz, B = 15.95 oz, and C = 15.94 oz, and all three fill distributions have population standard deviation = 0.1. We will use the information to see how the hypotheses tests perform, but not in conducting the tests. We randomly sampled n = 25 cans from each company in each of 50 states, and stored the resulting data in the file fill.mtw. Use File>Open Worksheet to load the data from u:\\msu\\course\\stt\\201\\s\\fill.mtw. Data for company A are in columns c1-c50, B in c51-c100, and C in c101-c150. Columns c1, c51, and c101 give data from state 1 (for companies A, B, and C respectively). Columns c2, c52 and c102 give the data from state 2 (for companies A, B, and C, respectively), and so on. Since company A is filling correctly, we make type I error if we reject H0 for it. The significance level, = .05, is the theoretical probability of making a type I error when using the test on samples from company A. On the other hand, we make type II error if we retain H0 for companies B and C, since they are under-filling. The symbol is used to denote the probability of making type II error. Since depends on the mean of the distribution from which we sample, will be different for companies B and C. We will compare those probabilities with the observed proportion of times such errors were made across the 50 states. A. In this part consider company A. We test fill levels across all 50 states, and then check how many states incorrectly reject the null hypothesis. 1. Which hypothesis is true for company A, H0 or Ha? [Hint: This is easy.] _________________________ 2. If we retain H0 for company A, then we make (circle one) a correct decision / type II error. 3. If we reject H0 for company A, then we make (circle one) a correct decision / type I error. Use Stat>Basic Stat>1-Sample T, samples are in columns c1-c50. Check the field \"perform hypothesis test\