STAT Show all of your work. As without work will not receive full condit Grading: Question 1 is worth point Question 2 is worth 6 points Question 3 is worth 3 points Submit your wers to Gradescope Problem: 1. Ar the following concept qution in 1-3 Bwork 5 Problemas Question 4 is worth points Question 5 is worth 5 points Question 6 is worth 4 points (a) sample likely to be exactly equal to the population mean? Explain why or why not (b) Will the sample mean (or sample proportion) always be inside a confidence interval for the population mean (or the population proportion)? Explain why or why not. (c) Setup: You obtain a dataset from a random sample. You double-checked your dataset, and there were no typos, and no mone All conditions were set to develop a confidence interval You develop a 50% condence interval for the population and your confidence interval is 482 < < 502 You double-checked your calculations, and everything was done correctly. Question: Later, you find out that the actual population doesn't your confidence interval contain the actual population? (d) Explain why you might want to potentially use the formulas when calculating the sample red when finding = 460. Why tead of interval for the population proportion. In the foranda, & prents the amount of er you are willing to accept, and represents the sample proportion 2. Setup: Suppo Canil wat out and obtained a sample of it (one serving). She is in the car contrat. She believe that the distribution of cake custent in appoximately The data that she collected is given below: Clario G Goal: Find a 13.5% upper confidence bound for the men calore content of the stand Procedures We caned out the analysis in R. Below is the output for 3 ditted that Potential R Output: OPTION ONE SAMPLE T-TEST data: fruit alternative hypothesis tru tn greater th 93.5 percent confidence interval 52.63746 alternative"", cond level 0.936) OSE SAMPLE T-TEST 11.136, at 2, alternative hypothesia: tru $3.5 percent confidence interval OPTION 3: >.test(fruit, alternative".", cond level = 0.936) ONE SAMPLE T-TERT 11.126, 10, -9.16-10 alternative hypothesis true mean is not equal to 93.5 percent confidence interval 61.25 **PROBLEM CONTINUED ON NEXT PAGE" Questionn (a) Which of the the option for the code would you need to use to identify the 93.3% upper (b) State the code bound from the code option that you chose. (c) Write an interportation of the interval that you found Make to include the content is your internation 1. For the following marios, identify whether you should use 2 or 1 in a confidence interval cakulation. (You don't have to do anything) (Scario 1) Mickey is tested in the agent of water boom carrying water badat could pour into a sider. It is believed that the amount of water carried in approchately ord. A mandom sample of 25 water backets was taken and it was found that, on average, ach back could hold 45 gallon of water, with a standard deviation of 02 gallo A 92% code interval wasted (Scenario 2) Minnie was a boutique that all hal-hows and bow-time. On a aldag ditated with a standard deviation of $0.72 Misted in the age selling price of products mild one day. A sample of 36 salos ot that day, and it was found that the go selling price was $4.78. A confidence interval was coated. 4. A comtration in public drinking water supplies is a potential risk. Drinking water armonic comtration (ppb) for various tropolitan rivers were tested. Ments we taken the at a drinking water facility upet of the metro ano, or at a drinking water facility dow Metro-Acea 26225 D40 38 23 21 20 12 118 Good: Find 98.17% cot Procedures We carried out the analysis. Below is the output for 3 difft ways the data could be any and Potential RO upata