EC 234 - Group Assignment 2 – Spring 2015
due by Monday, June, 1 @ 10.00
· Recall that each team has been assigned a number. When answering the questions, put your team number in the places where it says yourteamnumber. If you do not know your team number, please contact Damla Erhan.
· It is highly recommended that you use the basic functions of Excel (like finding averages) to speed your computations. You are also encouraged to use the more complicated statistical functions (like doing t tests) of Excel. The results of the tests in Excel and the ones you would compute on your own would be similar.
· If you have a “ghost” teammate who did not show up for meetings and did not contribute to the assignment at all, please leave out his/her name from the list of contributors.
· You must print and bring the answer sheet to the postbox of Damla Erhan in the Department of Economics. The answers must be typed in the spaces between the questions. You can adjust the amount of space between the questions to fit your answers. You don’t need to send the excel file and/or your computations.
Team number: ______
Team member names and ID’s:
Last Name / First Name / ID1.
2.
3.
Questions & Answers
You have two data columns to be selected from the data sheet: the first one is called yourteamnumber1, and the second one is called yourteamnumber2. For example, if you are team 49, then your data are in columns fortynine1 and fortynine2.
Both of these samples are composed of independent random draws from normally distributed populations with unknown means and unknown variances. These unknown variances are assumed to be equal.
PART I: The first set of questions are about the sample yourteamnumber1.
1. What is the maximum likelihood estimate for the population mean?
2. Calculate a 95% confidence interval estimate for the population mean.
3. Calculate a 95% confidence interval estimate for the population variance using S2 as an estimator of the population variance.
4. Test the null hypothesis that the population mean is equal to yourteamnumber (for example, if your team number is 49, then your null hypothesis will be that the population mean is equal to 49) against the two-sided alternative at 1% level of significance using the test statistic presented in class (method 1). Do not forget to write the hypotheses.
5. Test the null hypothesis that the population variance is equal to 1 against the two-sided alternative at 5% level of significance using the test statistic presented in class (method 1). Do not forget to write the hypotheses.
PART II: In the following set of questions, compare samples yourteamnumber1 and yourteamnumber2.
6. Calculate a 95% confidence interval estimate for the difference between the two population means.
7. Calculate a 90% confidence interval estimate for the ratio of the two population variances (yes, we assumed them to be equal, but would like to make sure).
8. Test the null hypothesis that the two population means are equal against the alternative that yourteamnumber1 has comes from a population with a larger mean than yourteamnumber2 at 1% level of significance. Do not forget to write the hypotheses.
9. Test the null hypothesis that the two population variances are equal against the alternative that yourteamnumber1 has comes from a population with a smaller variance than yourteamnumber2 at 1% level of significance using the test statistic presented in class (method 1). Do not forget to write the hypotheses. (Again, yes, we assumed the variances to be equal, but we would like to make sure anyway.)
Note for Excel Use:
5