**Comparing Populations Using Statistical Inference**

**Resources**

- Comparing Populations Using Statistical Inference Scoring Guide.
- APA Style and Format.
- Capella Writing Center.
- Yahoo! Finance.
- Hypothesis Tester | Transcript.
- Hypothesis Tester – Single Sample.
- Mall Time Results.

For this assignment, you will practice applying statistical inference to business decision scenarios.

**Practical Application Scenario 1**

Using the Yahoo Finance Web site as in Module 1, download a separate five years of daily data for a stock that begins with the first letter of your first name this time. Be sure that you match the exact dates that you used for the initial stock data, so that you can combine the spreadsheets by pasting.

Now, you are interested in seeing if the mean daily closing volume of the two stocks are statistically different when accounting for daily volatility of the market. In other words, you want to conduct a matched t-test using **Date** as the variable for pairing. To complete this analysis, do the following:

- State the null and alternative hypotheses via both an explanation and a math equation.
- Identify the appropriate statistical test. State this clearly.
- Conduct the test and state whether to accept or reject the null hypothesis using the p-value and an alpha of .05. You may solve the equation manually, use the Hypothesis Tester – Single Sample file provided in Resources, or use the SAS Enterprise Guide. You may also use the Hypothesis Tester multimedia piece provided in Resources to review the process for this equation.
- Report the rejection or acceptance of the null in terms of the scenario results using laymen’s terms. For this scenario, write a three-sentence paragraph that details why you can be statistically confident that the mean adjusted closing price has increased, decreased, or remained the same, and what would happen if alpha was .01.

You will need to use Excel or SAS to complete this test.

**Practical Application Scenario 2**

Now, use only the original stock data, those data associated with the first letter of your last name. You are interested in whether the mean daily adjusted closing price for the last three years has increased from the mean daily closing price of the first two years. Conduct a hypothesis test by doing the following.

- State the null and alternative hypotheses via both an explanation and a math equation.
- Identify the appropriate statistical test. State this clearly.
- Conduct the test and state whether to accept or reject the null hypothesis using the p-value and an alpha of .05. You may solve the equation manually, use the Hypothesis Tester – Single Sample file provided in Resources, or use the SAS Enterprise Guide. You may also use the Hypothesis Tester multimedia piece provided in Resources to review the process for this equation.
- Report the rejection or acceptance of the null in terms of the scenario results using laymen’s terms. For this scenario, write a three-sentence paragraph that details why you can be statistically confident that the mean adjusted closing price has increased, decreased, or remained the same, and what would happen if alpha was .01.

You will need to use Excel or SAS to complete this test.

**Practical Application Scenario 3**

You are interested in knowing whether there are differences in the mean daily adjusted closing price for a specific stock. For this practical application, go back to Yahoo! Finance and download five-years of monthly data for the stock beginning with the first letter of your last name. To do so simply requires you to change the frequency to monthly. Then conduct a test to see whether there are monthly differences in the mean adjusted closing prices.

- State the null and alternative hypotheses via both an explanation and a math equation.
- Identify the appropriate statistical test. State this clearly.
- Conduct the test and state whether to accept or reject the null hypothesis using the p-value and an alpha of .05. You may solve the equation manually, use the Hypothesis Tester – Single Sample file provided in Resources, or use the SAS Enterprise Guide. You may also use the Hypothesis Tester multimedia piece provided in Resources to review the process for this equation.
- Report the rejection or acceptance of the null in terms of the scenario results using laymen’s terms. For this scenario, write a three-sentence paragraph that details why you can be statistically confident that the mean adjusted closing price has increased, decreased, or remained the same, and what would happen if alpha was .01.

**Assignment Submission**

You must submit two documents. First, you must compile all of your answers in a Microsoft Word file, pasting in the tables and graphics you created to demonstrate your work (submitted as a .docx file). Second, you must upload the raw data (as a .csv file) that you used to do your analysis for the purposes of instructor replication. Failure to upload the second file will result in a score of zero on the assignment until the file is submitted. Assignments must be submitted to the assignments area for grading. Work e-mailed or otherwise presented cannot be graded in accordance with Capella grading standards. Because of the nature of statistics-based assignments, your instructor cannot give feedback on drafts of your work. Instead, if you have questions as you complete assignments, you are encouraged to attend the weekly supplementary instruction sessions or to consult the archived sessions for suggestions. Refer to the scoring guide prior to submission to ensure you meet all evaluation criteria.