Hypothesis Testing 1

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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.

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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. 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 emailed 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. Additional Requirements Compile your work and report in a 1–2 page Microsoft Word file: • Paste in the tables you used to make your calculations. • Clearly title your tables, including each row and column. • Highlight the results of your data calculations within each table. Hypothesis Testing 1 Scoring Guide Criteria Proficient Distinguished Determines an accurate and appropriate null hypothesis and alternative hypothesis for Determine the null hypothesis and Determines the null hypothesis and making decisions alternative hypothesis for making alternative hypothesis for making regarding pricing. decisions regarding household decisions regarding household Explains the income. income. hypothesis statements and accurately expresses the mathematical equations of the hypotheses for testing. Compute the appropriate statistical test to determine acceptance or rejection of a null hypothesis. Computes the appropriate statistical test to determine acceptance or rejection of a null hypothesis. Computes the appropriate statistical test to determine Criteria Proficient Distinguished acceptance or rejection of a null hypothesis, and justifies the response. Computes and interprets the pvalue to indicate acceptance or rejection of a null hypothesis regarding average customer spending, reports the findings, and justifies the interpretation. Compute the p-value to indicate acceptance or rejection of a null hypothesis regarding average household income. Computes the p-value to indicate acceptance or rejection of a null hypothesis regarding average household income. Compile findings into a management report with details for recommended actions. Compiles findings into a management report with details Compiles findings into a for recommended management report with details for actions; presents recommended actions. information in a format expected of the business profession. Communicate in a manner that is professional and consistent with expectations for members of the business professions. Communicates in a manner that is professional and consistent with expectations for members of the business professions. Communicates in a manner that is professional, scholarly, and consistent with expectations for members of the business professions. Adheres to APA guidelines, and work is appropriate for publication. Hypothesis Tester – Single Sample Hypothesis Test for a Population Mean, Sigma Known If the population standard deviation is known, we can directly calculate the standard deviation of the sampling distribution (the standard error of the estimate), and use the standardized normal distribution to get a z-multiple, using the Excel function NORMSINV. We can then calculate p for each of the three possible test conditions, and compare it to each level of alpha to see whether the null hypothesis should be rejected. Inputs: Hypothesized population mean: Population standard deviation (sigma): Sample size (n): Sample mean (x-bar): 295 12 50 297,6
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Running head: HYPOTHESIS TESTING 1

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Hypothesis Testing 1
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HYPOTHESIS TESTING 1

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Hypothesis Testing 1

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From the information presented, it is captured that Boos Allen was confident regarding
the analysis of the 2010 sample that the population mean was $119,155 and the standard
deviation being $30,000. From the information presented, the sample mean is als...


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