Introduction: One of the goals of this course is that you will be able to perform hypothesis tests. ...

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Introduction: One of the goals of this course is that you will be able to perform hypothesis tests. In this project, you will demonstrate your understanding of all the steps involved in testing a hypothesis test of ? when ? is unknown. Directions: Conduct the hypothesis test described in the SCENARIO below. Write up the process and the test results in a professional-quality report using Microsoft Office. Include the following elements in your 1–2-page written report: 1) INTRODUCTION: Describe the scenario and the reason why the LEGO Group's line manager should perform a hypothesis test. 2) BODY: Include the following elements in the body of the report: a) The name of the appropriate hypothesis test (e.g., “1 Sample Proportion Z test,” “1 Sample T-Test for Means”, etc.) b) The null and alternative hypotheses. (Be sure to first define the parameter in context.) c) Requirements check that justifies the use of the test: i) Is the sample a simple random sample? ii) Is the sample from a normal distribution, or does the Central Limit Theorem apply because ???? ? 30? d) Give all the test details, including the sample statistic, the test statistics, the critical value, and the p-value. e) Reject or fail to reject the null hypothesis f) Report the conclusion of the hypothesis test in context. g) Report and interpret the confidence interval estimate of the parameter in question h) Weave in answers to any specific elements requested in the SCENARIO below. 3) CONCLUSION: Write a brief conclusion to the report, giving your recommendations to the line manager on whether or not they need to take action to repair their machine. In the conclusion, please include your thoughts, from a Christian Worldview, on the importance of ethics and integrity in the process of performing all statistical tests. For example, why is it important that a researcher, a business owner, or a line manager handles data honestly so that the statistical results are accurate, even if the repercussions are difficult or costly repairs? 4) After completing the report, save the Word document as a PDF and upload to the Dropbox on D2L. SCENARIO: The LEGO Group, an international company, makes the LEGO blocks that many of us have played with as kids. Many of its products require that the production process performs according to specifications. One of the products is Little People. The neck diameter of each of the Little People must be 0.5 inches so that it can be attached to the head properly. LEGO is interested in testing to see whether this process is performing according to specifications. If it is not functioning correctly, the LEGO Group will shut down the manufacturing process to fix the Little People machine. The line manager takes a random sample of 40 Little People heads. The average diameter of the sampled necks is 0.48 inches, with a standard deviation of 0.05 inches. Is there sufficient evidence that the machine is not working correctly? Use a two-tailed hypothesis test with a significance level of ?=0.02 to determine the answer. Give the confidence interval estimate for the actual population neck size of Little People. Use a 98% confidence level to align with the hypothesis test in part 2. Does “0.5 inches” appear in the confidence interval? Does the confidence interval estimate of the mean neck size, , of Little People align with the conclusion of your hypothesis test? Explain why the two methods for estimating match or don’t.