2. Noodle Dilemma (AKA the Too Long Spell) (25 Points) The process that makes the spaghetti noodles for Delectable Delights is supposed to produce noodles with an average length of 252.5 mm. Allison, the Quality Control Manager, is concerned that Machine #13 is not working properly and the noodles it produces are too long. You are asked to calculate a 90% confidence interval for the average length of Machine #13's noodles using the results of a random sample of 25 noodles. The measurements from these 25 noodles can be found in the file The Too Long Spell.jmp (a) Define the parameter of interest, it , in the context of the problem. [5 pts) (b) Have the conditions for calculating a confidence interval for a population mean been met?I Be careful. Your sample size is less than 30 thus you will need another way to verify whether or not you can consider the sampling distribution for the sample mean to be approximately normally distributed. Review page 149 in the lecture guide. The instructions on how to do this in JNIP is found in the file M Normal Probability Plot Instructions. When you answer this question, include the graphics provided by JM'P. (5 pts) (c) The output from part (b} includes a Statistics Surmnary Table which reports a 95% confidence interval for the average length of Machine #13'5 noodles. To change this to a 90% confidence interval select the red triangle next to the Summary Statistics Table and select Customize Summary Statistics. At the bottom of the list in the dropdown menu change the confidence level from .95 to .90. Copy and paste the resulting Summary Statistics table showing the 90% confidence interval. (5 pts} (d) Interpret the confidence interval you found in part (c). Round the lower and upper bounds of the interval to 1 decimal place. [5 pts) (e) Using the condence interval that you found, do you believe that Machine #13 is making noodles that are on average too long? (5 pts)