# Hypothesis Testing 1

• Solve four equations based on a scenario related to hypothesis testing. Demonstrate your method, report your findings, and write a brief paragraph that details your recommendations for action.Note: The assessments in this course build upon each other, so you are strongly encouraged to complete them in sequence.SHOW LESSManagers can use sampling techniques to make managerial decisions and draw conclusions. The statistical technique that we will use to evaluate the samples is hypothesis testing; mathematically speaking, we will use statistical techniques to evaluate the likelihood of an assertion.By successfully completing this assessment, you will demonstrate your proficiency in the following course competencies and assessment criteria:
• Competency 1: Evaluate the quality and fit of data for use in business analysis.
• Determine the null hypothesis and alternative hypothesis for making decisions regarding household income.
• Competency 3: Analyze business decision opportunities using basic inferential statistics.
• Compute the appropriate statistical test to determine acceptance or rejection of a null hypothesis.
• Compute the p-value to indicate acceptance or rejection of a null hypothesis regarding average household income.
• Competency 5: Apply data analysis to general business management planning and decision making.
• Compile findings into a management report with details for recommended actions.
• Competency 6: Communicate in a manner that is professional and consistent with expectations for members of the business professions.
• Communicate in a manner that is professional and consistent with expectations for members of the business professions.
##### Competency Map

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### Context

Managers use hypothesis testing and statistical techniques to evaluate the likelihood of an assertion. Hypothesis testing is at the core of inferential statistics. It is the foundation of the inferential statistics used to help managers make better decisions. A typical managerial decision using hypothesis testing would be to compare samples of purchased products to ensure they conform to firm quality standards. In fact, sampling itself is a particularly useful data analysis technique. Malls and stores often sample prospective customers. So do retail fast food franchises—take a look at the bottom of your receipts the next time you purchase something.

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### Questions to Consider

To deepen your understanding, you are encouraged to consider the questions below and discuss them with a fellow learner, a work associate, an interested friend, or a member of the business community.

• Why is it important that a sample be random?
• For its validity, all hypothesis testing depends heavily on the assumption that the sample that is used was drawn using probability sampling techniques. Why is this important?
• What can you do if you cannot use a probability sampling technique? (For example, suppose there is no good sampling frame available for the population of interest.)
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### Resources

#### Required Resources

The following resources are required to complete the assessment.

##### Capella Resources

Click the link provided to view the following resource:

• ### Assessment Instructions

Use the Hypothesis Tester – Single Sample file (linked in the Resources under the Required Resources heading) and data analysis software to complete the calculations for this scenario.You may also refer to the Hypothesis Tester – An Introduction media piece (linked in the Resources under Suggested Resources) to review the process for computing this equation.

#### Practical Application Scenario

In 2010, Playbill Magazine, a regionally based magazine, consulted Boos Allen to determine the mean annual household income of its readers. Using a list of customers provided by Playbill, Boos Allen randomly sampled 300 Playbill customers. From that sample, Boos Allen is confident that the average Playbill reader’s household income is \$119,155, with a population sample household income standard deviation of \$30,000.Recently, two Playbill executives suggested that the mean average household income for Playbill readers has increased, and the magazine price should be raised. As new marketing manager for Playbill, you convince the chief operating officer to complete a second survey with Boos Allen to confirm that assertion. Yesterday, the new Boos Allen report appeared on your desk. From a new sample of Playbill customers, taken from a list of recent customers you e-mailed to Boos Allen, the 2012 Playbill customer profile shows a mean annual household income of \$124,450, with a population standard deviation of household income unchanged at \$30,000.You realize that you have enough data to perform a one-sample hypothesis test. In order to choose the correct statistical tool to complete this assessment, consider the following questions:

• What do you know about the population being studied? (For example, do you know the standard deviation of the overall population?)
• What do you know about the population sample you chose? (For example, which sample statistical parameters do you have, such as mean, standard deviation, variance, and so on?)

#### Directions

Solve the following equations, based on the data from the Hypothesis Tester – Single Sample file. Demonstrate your method and display your results in table format, using Excel or another appropriate computer application.

1. Identify the null hypothesis, via both a written explanation and a math equation.
2. Determine the alternative hypothesis, via both a written explanation and a math equation.
3. Solve the equation to determine whether to accept or reject the null hypothesis.
4. Determine whether the p-value indicates acceptance or rejection of the null. Use alpha = .05.

Next, address the following in a report to the executives:

• Write a three-sentence paragraph that details your recommendations for a course of action, based on your results.
• Report the rejection or acceptance of the null, in terms of the scenario results.
• Explain why you can be statistically confident that the mean household Playbill reader’s income has increased, decreased, or remained the same.
• State whether you would propose that the cost of the magazine be raised.
• Describe what would happen if alpha was .01.