Question
Can someone pls answer 1-6? In this lab we will perform testing of hypotheses related to the population mean. This material is in Section 13.2.
Can someone pls answer 1-6?
In this lab we will perform testing of hypotheses related to the population mean. This material is in Section 13.2. Download the worksheet for this lab, fill.mtw, from LON-CAPA to your computer. 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 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", and enter value 16 into the "hypothesized mean" field. We would like to test H0 : = 16 vs. Ha : < 16. Click on Options and select the alternative "mean is < hypothesized mean". The results will be displayed in the session window. To avoid printing delays, you are given a printed copy of all Minitab output at the end of the lab paper. For the rest of this step, use that part of the Minitab output for company A. Check Minitab's work for the state # 10, c10, for company A. Use the values of sample size (n), sample mean ( x ) and sample standard deviation (s) listed on Minitab's output under N, Mean, StDev to calculate the standard error of the sample mean and test statistic using formulas provided below. The null (hypothesized) value of the sample mean in the hypothesis test is 0 16. 4. Sample mean x _________________________ 5. Standard error = s/ n ____________________________________________ 6. Test statistic s n x t / 0 ______________________________________________________
Step by Step Solution
There are 3 Steps involved in it
Step: 1
Get Instant Access to Expert-Tailored Solutions
See step-by-step solutions with expert insights and AI powered tools for academic success
Step: 2
Step: 3
Ace Your Homework with AI
Get the answers you need in no time with our AI-driven, step-by-step assistance
Get Started