Guide for group projects 2

ECO 320 – Mathematical Statistics

Important note: This document is meant to give the ground rules for Group Projects. If you fail to comply with any of the rules listed in this document, you may get only partial or no credits for your project. If you have any questions, post it on the relevant thread on the discussion board. I will not answer emails with general interest questions about the Group Projects.

- Refer to the previous document for a general guide about the Group Project.

- You must use the same data you have used for Group Project 1. You can integrate them with additional data, if necessary. If you want to change your data you must consult with me first.

- You must use the material of \Introduction to Hypothesis Testing” and \More on Hypothesis Testing” for Group Project 2.

- You are expected to upload your project on Blackboard, where a new Assignment will be created for this purpose (the \proxy” will upload the project, there is no need to upload the project several times). In particular, you must upload a zip le containing the following (the contribution of each item to the Group project grade is included between brackets):

- The data you have used in excel format, along with a description in pdf (5%).

- A word or pdf document of minimum 2 (two) double-spaced pages, edited for spelling and grammar mistakes, in which you explain what you have done with clarity. This should be structured as an essay. This page provides a great step-by-step guide to write a good essay in Economics. You should try to follow these guidelines as closely as possible. This document must include:

- A brief summary of the variable of interest, population and sample used in Group Project 1, as well as the conclusion obtained from the
- Confidence Interval for the mean (5%).

- Consider a one-tail test for the population mean: (25%)

{Consider a upper-tail test. Moreover, assume that the population variance is unknown, what are the implications of this assumption? (if you do not observe the population variance, assume it is equal to the sample variance).

{Define the null and alternative hypothesis for a hypothesized value equal to the value of the second observation in your sample.

{Fix the level of significance equal to:0.05

Find the critical value for your test.

{Formulate the decision rule for your test and explain the result.

{Represent in a figure the critical value and rejection region for your test, and use the figure to justify whether you reject or not the null hypothesis.

- Suppose that the true population mean is equal to the value of the first observation in your sample: (25%)

{Fix the level of significance equal to: 0.1

{Compute the power of the test in (b) for the new. Explain the result. {What is the probability of a Type II error? Explain the result.

- Consider a two-tail test for the population mean: (25%)

{Assume that the population variance is unknown. What are the implications of this assumption?

{Define the null and alternative hypothesis for a hypothesized value equal to the value of the third observation in your sample.

{Fix the level of significance equal to:0.

{Find the critical values for your test.

{Formulate the decision rule for your test and explain the result.

{Represent in a figure the critical values and rejection regions for your test, and use the figure to justify whether you reject or not the null hypothesis.

{Find the test statistic for your two tail test, and indicate whether you reject or not the null hypothesis.

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