Now there is something the employees of Delectable Delights do not know. Arthur Weasley of the Ministry of Magic has twin sons, Fred and George, who are working on perfecting the Too Long Spell for their joke shop. The spell would make things, well, too long. They wanted to test it out and used the spell on Machine #13 to see if the Too Long Spell would cause the machine to make the spaghetti noodles too long. It was a success! The Too Short Spell (25 points) The Weasley boys started to sell their new product. Unfortunately, someone tried it out on the Hogwarts School of Witchcraft and Wizardry cat Mrs. Norris. (They never could figure out who could possibly be so crazy as to try to put a spell on Mrs. Norris). Mrs. Norris' fur began to grow too long, and it seemed it would never stop growing! You should have seen the nasty hairballs! The caretaker Argus Filch was beside himself with worry. To resolve the situation, the boys decided to counteract the Too Long Spell with a Too Short Spell. Not wanting to further upset the caretaker if the spell didn't work, they tried it out on Machine #13 to see if the noodles would be the correct length again. The spell worked, but it worked too well and the noodles from #13 were suddenly way too short. Allison asks you to perform a hypothesis test at a 5% signicance level to see if the noodles from #13 are on average too short. A random sample of 41 noodles is selected from the machine. The measurements from these 41 noodles can be found in the file The Too Short Spell.jmp. Use the following steps to perform this hypothesis test using the Rejection Region approach. Use a significance level of 5%. (a) Define p in the context of the problem and state the appropriate hypotheses. (5 PS) (b) State and check the conditions for a hypothesis test of the mean. (5 pts) (c) Use JMP help to calculate the value of the test statistic. Using the data in the file The Too Short Spell.jmp select Analyze >> Distribution. Set the column with the noodle lengths to be the Y,Columns and select OR. Select the red triangle next to the column name and choose Test Mean. Fill in the box Specify the Hypothesized Mean with the value of no . Do not ll in any other information. Select OK. Copy and paste the portion of the output showing the value of the test statistic here