Posted: May 16th, 2023

The manager of a large manufacturing company claims that the mean income for all his senior

STAT 121: Writing Assignment 2Significance Test and Confidence Interval (24 points)Directions: Read the following problem, and follow directions, and answer each question completely but concisely. Be sure to save a copy of your work, and see the syllabus for submission details. (The spacing between the questions is not necessarily an indication of the expected response length.)The ProblemThe manager of a large manufacturing company claims that the mean income for all his senior assembly-line workers is $500 per week. The workers believe that the mean wage is actually less than $500 and decide to test their manager's claim. A random sample of 16 workers had the following weekly incomes: 495470475480485500465475490495505510485490460490You may use any statistical software to answer the following questions. (Note:.byu.edu/statcrunch/index.html">http://statistics.byu.edu/statcrunch/index.html can be used for this problem [Passcode: BYUStat].) Part A. Test of SignificanceSTATE:At the ? = 0.05 level, is there sufficient evidence to conclude that the mean weekly salary of all senior assembly-line workers is less than $500 per week?PLAN:1. State the name of the appropriate test procedure you will use (e.g., matched-pairst-test for means). (1 pt)2. Describe the parameter of interest in the context of the problem. (1 pt)3. State the null and alternative hypotheses. (2 pts)4. State level of significance. (1 pt)SOLVE:5. Include a plot of the data. Comment on whether it has one peak and whether there are outliers. (1 pt)6. Listand check the conditions for the test procedure you named above. (4 pts)7. UseStatCrunch to get the values of the sample mean and sample standard deviation. (1 pt)8. State the test statistic value (including your calculations) and the associatedP-value using the appropriate table, not from statistical software. (2 pts)CONCLUDE:9. Answer the question posed in theSTATE step in context. Do this by including these three parts in your conclusion (3 pts):• CompareP-value with ?.• Decide whether to “rejectH0” or “fail to rejectH0.”• State your conclusion in context.Part B. Confidence Interval EstimationSTATE:What is a 95% confidence interval estimate of the mean weekly salary of all senior assembly-line workers in this manufacturing company?PLAN:1. State the name of the appropriate estimation procedure (e.g. matched-pairst-confidence interval for estimating the mean difference). (1 pt) (Note: You have already described the parameter being estimated in part A, so you don't have to repeat it here.)2. State the confidence level. (1 pt)SOLVE:(Note: You have already plotted the data and checked the conditions in part A, so you don't have to redo it here.)3. Restate the values of the sample mean and sample standard deviation. (1 pt)4. Write down thet* critical value. Calculate and record the confidence interval in interval form. Be sure to show your work. (2 pts)CONCLUDE:5. Interpret your confidence interval in context. Do this by including these three parts in your conclusion (3 pts):• Level of confidence• Parameter of interest in context• The interval estimate

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