Section 9 Lab Part 2 key

STAT 3090 S ECTION 9 L AB F ALL 2023 H YPOTHESIS TESTING FOR ONE OR TWO MEANS . N AME : Key O BJECTIVES : Upon completion of this project, you should be able to:  State and verify the conditions necessary for a hypothesis test for a population mean, paired t-test, and for two independent means,  Perform a hypothesis test for a population mean using the p-value approach and rejection region approach  Perform a hypothesis test for a paired t-test using the p-value approach and rejection region approach  Perform a hypothesis test for two independent population means using the p-value approach.  Use JMP to perform Hypothesis Tests for means,  Draw conclusions about the population based on the results of a sample Delectable Delights is a large consumer food manufacturer selling its products in retail stores nationwide. You have landed your first job after graduation from Clemson in their advertising division. Since you took statistics as a part of your coursework, you are often called upon to perform data analysis for the advertising division, as well as other divisions of the company. D IRECTIONS : Answer the following questions using complete sentences as though you were presenting your analysis to the employees of Delectable Delights. Please provide any appropriate output and/or screenshots from JMP. Instructions for creating several types of graphs or tables and statistics can be found on Canvas in the file JMP Instructions.docx . Paste your answers and any output into this document. Day One: Hypothesis Test for population mean 1. The Too Short Spell (40 pts) Recall from the section 8 lab that 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, was concerned that Machine #13 was not working properly and the noodles it produced were too long. You found that indeed Machine #13 made the noodles to long. 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. 1

STAT 3090 S ECTION 9 L AB F ALL 2023 H YPOTHESIS TESTING FOR ONE OR TWO MEANS . It was a success! The Weasley boys started to sell their new product, a spell that would make things too long. 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% significance 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 and JMP to perform this hypothesis test using the Rejection Region approach. Use a significance level of 5%. You will then use the P-Value approach for this same problem. (a) Define μ in the context of the problem and state the appropriate hypotheses. (5 pts) Let μ be the true average length of the spaghetti noodles form Machine #13. H 0 : μ = 252.5 mm H 1 : μ < 252.5 mm 1 pt for defining μ in context 1 pt for using μ in the hypothesis statements 1 pt for correct value of μ 0 1 pt for equal sign in null hypothesis 1 pt for less than sign in alternative hypothesis (b) State and check the conditions for a hypothesis test of the mean. (5 pts) As stated in the problem, the noodles were randomly selected. Since the sample size of 41 is greater than or equal to 30, we can assume that the sampling distribution of x is approximately normally distributed. ̅ 2 points for statement indicating that the sample was randomly selected 2

STAT 3090 S ECTION 9 L AB F ALL 2023 H YPOTHESIS TESTING FOR ONE OR TWO MEANS . 2.5point for comparing the test statistic from part (c) to the rejection region 2.5 point for rejecting the null hypothesis (f) Write a final concluding statement about the results of the hypothesis test. (In other words, write the final summary statement.) (5 pts) At the 5% significance level, there is sufficient evidence to suggest that the true mean length of spaghetti noodles from Machine #13 are shorter than 252.5 mm. 1pt for context that includes the parameter of interest 1pt for stating conclusion in terms of the alternative hypothesis 3 pt for correct conclusion based on part (e). (g) Look back at the JMP output in part (c). The JMP output gave you three p-values. For the hypothesis test defined in part(a), which is the correct p-value? (5 pts) Prob<t <.0001 This is correct or incorrect (h) Explain how to use the p-value in part (g) to determine if you should reject the null hypothesis or fail to reject the null hypothesis. (5 pts) Since P-value =0.0001 < α = 0.05 , we reject H 0 . This is correct or incorrect – students’ wording will vary As you can imagine, the employees at Delectable Delights are quite concerned about the performance of machine #13. To be continued … 2. WebAssign Section 9 Hypothesis Tests Means #1 (14 points) To do this problem, use JMP. 1. Copy your data table from WebAssign, and paste it into a new data table in JMP. 2. Your JMP Data Table should look something like the one below 4

STAT 3090 S ECTION 9 L AB F ALL 2023 H YPOTHESIS TESTING FOR ONE OR TWO MEANS . 3. You will need to get all of the data into one column. To do this go to a. Table >> Stack and put each column into the Stack Columns field. Select OK . b. You will get a new data table that looks similar to the one below. Use the column with the data values to complete the problem. Note if you need to enter the not equal to sign, simply type != as in the directions. 3. WebAssign Section 9 Hypothesis Tests Means #2 – 7 (22 pts) Day Two: Hypothesis Tests for matched pairs (paired t-test) and two independent samples 5