Computer Readiness and Hypothesis Testing
This is a preliminary assignment using Microsoft Excel’s Analysis Toolpak and the statistical package SAS to solve a statistical inference problem. As you work, keep in mind you are collecting results in a single word processing file to be saved as a Word file
How to do it:
1. View the Quick Start Guide to SAS in the Cloud located on my personal site. Work through this Quick Start Guide and save your SAS commands (“SAS code” or “command file”) and statistical results. Be sure to save the results you get, near the end of the Quick Start Guide, when you deliberately make SAS mistakes.
2. Having done the work so far to familiarize yourself with how Excel and SAS statistical tools work, now consider the problem at hand: advising employees who participate in a firm’s 401(k) investment program. Two different kinds of investments are available: (1) actively managed funds, which hire managers who conduct analysis and seek the best investments; and (2) passively managed funds that only seek to track market indexes, thereby getting an average return before expenses.
3. One possible null hypothesis is that active and passive investors have the same long-term return. After conducting some online research and before looking this problem’s data set, answer in words and explain: What is a reasonable alternative hypothesis? Cite any online sources that you use.
4. Bring up Microsoft Excel and install the Analysis Toolpak. Directions are located at https://support.office.com/en-us/article/Load-the-Analysis-ToolPak-305c260e-224f-4739-9777-2d86f1a5bd89 (Links to an external site.)Links to an external site.. For earlier versions of Excel, the toolpak works just the same way, but you will need to find directions for your own older version.
5. From the Canvas site’s Files, download data01.xlsx and open it in Excel. Using the Analysis Toolpak you just installed, choose Descriptive Statistics and OK. Enter the data range b2..b32 and check the box for Summary Statistics. Click OK, and you should now have a summary statistics table for the variable RETURN, which equals each participant’s rate of return for a specified period. You’ll be putting this table into the document you submit at the end of this assignment.
6. The constructed data set data01.xlsx reflects the experience of employees who invested in their firm’s 401(k) plan. PASSIVE is a variable equal to 1 for those who invested in the passive option, and equal to 0 for those who invested in actively managed funds. The null hypothesis is H0: m0 = m1 . In symbols, what is your alternative hypothesis?
7. Now Microsoft Excel’s Tools Data Analysis to calculate Descriptive Statistics (check the Summary Statistics option) separately for the passive and active investors. Hang onto both sets of summary statistics to turn in.
8. Set up a two-tailed test of the hypothesis that for the non-passive investors only (those with PASSIVE = 0) the average return is 4.14 percent. (H0: m1 = 4.14). Show all calculations for the test statistic, remembering that it equals the [(actual value of the sample mean minus the value it would have under the null hypothesis), all divided by the calculated standard error]. Report whether or not you reject the null hypothesis at the 5 percent significance level. Using the computer or a pen at your option, draw a graph to illustrate your test.
9. Set up a one-tailed test of the null hypothesis that the average return of the non-passive investors is greater than or equal to 4.14. (H0: m1 ≥14). Report whether or not you reject the null hypothesis at the 5 percent significance level. Using the computer or a pen at your option, draw a graph to illustrate your test.
10. Next, use Microsoft Excel to do a two-sample test of the null hypothesis that there is no difference in returns between active and passive investors. Be sure to use the “t-Test: Two-Sample Assuming Unequal Variances” analysis tool under Tools Data Analysis. You will enter the cells for one group as “Variable 1” and the other group as “Variable 2.” Hang on to the results of this test to turn in. You do not need to provide any commentary on this test.
11. Finally, use SAS to run a difference of means test on this data set. Keep your SAS command file and results of this test, and save them to turn in as part of your file. You will probably need to consult the full SAS guide located on Canvas to get the necessary commands to run this test. You do not need to provide any commentary on this test.
One additional note: Because of differences in the null hypothesis, do not expect that you will get identical t-statistics when you do the different versions of this test.
What to turn in:
In a single Word .docx file, submit your answers to the questions. Include, in this order:
• a description and error messages from the mistakes you generated in the SAS Quick-Start Guide
• the result of running the SAS Quick-Start Guide problem
• your answer the question about active vs. passive investors, with citation
• the table of descriptive statistics from the full sample and the active and passive parts
• full support for your calculated t-statistics in the hypothesis tests
• drawings of your hypothesis tests (use a computer, or draw and then take a picture with your phone).
• results of your Excel two-sample hypothesis test
• your SAS command file from the final question
• SAS results from the final question
1. Be sure to carefully cite any online sources that you use
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