# Hypothesis Testing Using One Sample

For this practical application assignment, you will use the daily adjusted closing price data you downloaded in Module 1 (AliBaba was the stock needed for five years of prices but it’s attached) . You may use the Hypothesis Tester â€“ Single Sample document, linked in Resources, to complete both scenarios. You may also want to review the SAS One Sample T-Test tutorial, also located in the Resources.

#### Practical Application Scenario 1

Often, it is interesting to know whether mean adjusted closing prices have changed from some base value. Suppose you are interested in whether the mean adjusted daily closing price for the stock you downloaded in Module 1 has increased from some base price (for example, \$4 or \$10 or . . .). For our purposes, we will assume that you are interested in whether the mean daily adjusted closing price has increased from the oldest daily adjusted closing price in your dataset (for example, the one from five years ago). Conduct a hypothesis test that the mean adjusted daily closing price has increased from the base price. Assume that the stock price is sufficiently normal to conduct a t-test. Note: you might also transform the stock to normality, that is, applying the natural logarithm.

To successfully complete this hypothesis test, 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 Hypothesis Tester â€“ 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.
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.
5. Would the results of your hypothesis test be different if you used a Z-test rather than a t-test? Why or why not?

#### Practical Application Scenario 2

To explore your stock dataset, you decide that you want to know whether your stock’s mean daily volume has increased or decreased from the oldest closing value in your data set (in other words, the closing volume from five years ago). Often, you would conduct a test like this with two samples, but for now, we will just use the oldest closing value as the baseline. Conduct a hypothesis test to see if the mean daily volume differs from the oldest daily volume in your dataset. Complete 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 Hypothesis Tester â€“ 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.
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.