### Comparing Populations Using Statistical Inference

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.(JP Morgan) 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 paired t-test using Date as the variable for pairing. To complete this analysis, do the following:

1. State the null and alternative hypotheses via both an explanation and a math equation.
2. Identify the appropriate statistical test. State this clearly.
3. 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 Analysis ToolPak add-in for Microsoft Excel, or use the SAS Enterprise Guide.
4. 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 adjusted closing price of the first two years. Conduct a two-sample hypothesis test by doing the following.

1. State the null and alternative hypotheses via both an explanation and a math equation.
2. Identify the appropriate statistical test. State this clearly.
3. 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 Analysis ToolPak add-in for Microsoft Excel, or use the SAS Enterprise Guide.
4. 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, use the 5 years of daily data that you downloaded previously for the stock beginning with the first letter of your last name. Manipulate the data so that you have all of the daily stock data for the days in each month of the year together (for all 5 years), then conduct an ANOVA F-test to see whether there are monthly differences in the mean adjusted closing prices.

1. State the null and alternative hypotheses via both an explanation and a math equation.
2. Identify the appropriate statistical test. State this clearly.
3. 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 Analysis ToolPak add-in for Microsoft Excel, or use the SAS Enterprise Guide.
4. 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 income has increased, decreased, or remained the same, and what would happen if alpha was .01.

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