Part 1 - Hand work (all work and graphs must be done by hand). Instructions: Write your answers onto one or more sheets of paper or on a tablet. Include your name and EID at the top of each page file. To get full credit for each question, you must: Show your work. Include appropriate units with answers when relevant. . Round all numeric answers to at least 3 decimal places. Attach your Part 2 - R work below and submit your assignment as a single .pdf file to Gradescope by following the directions on Canvas. 1. Some types of nerve cells have the ability to regenerate a part of the cell that has been amputated. In a study of this process in lemurs, researchers cut nerves emanating from the spinal cord of a sample of 31 animals and measured the content of creatine phosphate (CP). They found a sample mean of 0.183 mg/g, with a standard deviation of 0.094 mg/g. In healthy cells, the CP content is 0.150 mg/g. Assuming all relevant assumptions hold, conduct the appropriate test to determine if CP content in regenerating nerve cells differs from this amount in this population of lemurs. Include all steps for full credit. Given: tay=go = 2.042 (4pt) 2. A patient's blood volume is often depleted after a major surgery, so a group of researchers designed a drug to increase plasma volume (in ml). They set up an experiment and measured the total circulating volume of blood plasma in a group of patients immediately after they had surgery, and then again one hour after an infusion of the drug into the bloodstream. a. In the perspective of a future patient who undergoes surgery, what would be the consequence of a Type-I error? (Ipt) b. In the researchers' perspective, what would be the consequence of a Type-II error? (Ipt) c. List a potential confounding variable for this study and briefly explain a possible impact it might have on the results. (?pp) 3. To investigate if autism is marked by different brain growth patterns in early life, studies have tried to link brain size in toddlers to autism. Suppose the whole-brain volume in non-autistic toddlers is known to be 1200 milliliters, on average. One study based on a sample size of 25 autistic toddlers had a sample mean volume of 1280 ml with a standard deviation of 230 ml. a. Calculate a 95% confidence interval for the whole-brain volume of autistic toddlers. Given: tay=24 = 2.064 (3pt) b. Do the results from this study suggest that autistic toddlers have a different mean whole- brain volume as non-autistic toddlers? Explain your answer. (2pt) c. If the data from this study had the same descriptive statistics but was from a sample of size 40 instead of 25, would the 95% confidence have been wider or narrower? (Ipt)