Data Analysis Assignment
Amanda Mueller
MBA6018 – Data Analysis
Unit 3 Activity 1
January 23, 2013
Practical Application Scenario 1
In 2010, Playbill Magazine contracted Boos Allen to conduct a survey aimed at determining the average annual household income of Playbill readers. 300 readers were randomly pulled and sampled from the list of customers provided by Playbill Magazine. From that sampling effort, Boos Allen was confident that the population average household income is $119,155 and that the population sample household income standard deviation is $30,000.
Two Playbill executives recently hypothesized that the average annual household income of its readership has increased and so believe that the magazine price should also increase. From a 2012 sample, Boos Allen has profiled the new average annual household income to be $124,450 with a population standard deviation unchanged at $30,000. To determine if this hypothesis is valid, using the α value of 0.05, the following steps are taken:
Step 1: State the null hypothesis H0 and the alternative hypothesis Ha
The null hypothesis is the statement being tested (pg 349). In this scenario, it can be defined as a household income of less than or equal to $119,155 for the average Playbill reader. Mathematically, this can be represented as H0: μ ≤ $119,155. This hypothesis holds that if the new annual average household income is found to be equal to or less than the 2010 value of $119,155, the price of the magazine should not be increased (H0 should not be rejected).
The alternative hypothesis is the statement that will be accepted only if there is strong enough sample evidence that it is true (pg 349). In this scenario, it can be defined as a household income of greater than $119,155 for the average Playbill reader. Mathematically, this can be represented as Ha: μ > μ0 or Ha: μ > $119,155. This hypothesis holds that if the new annual average household income is found to be greater than the 2010 value of
MBA6018 – Data Analysis
Unit 3 Activity 1
January 23, 2013
Practical Application Scenario 1
In 2010, Playbill Magazine contracted Boos Allen to conduct a survey aimed at determining the average annual household income of Playbill readers. 300 readers were randomly pulled and sampled from the list of customers provided by Playbill Magazine. From that sampling effort, Boos Allen was confident that the population average household income is $119,155 and that the population sample household income standard deviation is $30,000.
Two Playbill executives recently hypothesized that the average annual household income of its readership has increased and so believe that the magazine price should also increase. From a 2012 sample, Boos Allen has profiled the new average annual household income to be $124,450 with a population standard deviation unchanged at $30,000. To determine if this hypothesis is valid, using the α value of 0.05, the following steps are taken:
Step 1: State the null hypothesis H0 and the alternative hypothesis Ha
The null hypothesis is the statement being tested (pg 349). In this scenario, it can be defined as a household income of less than or equal to $119,155 for the average Playbill reader. Mathematically, this can be represented as H0: μ ≤ $119,155. This hypothesis holds that if the new annual average household income is found to be equal to or less than the 2010 value of $119,155, the price of the magazine should not be increased (H0 should not be rejected).
The alternative hypothesis is the statement that will be accepted only if there is strong enough sample evidence that it is true (pg 349). In this scenario, it can be defined as a household income of greater than $119,155 for the average Playbill reader. Mathematically, this can be represented as Ha: μ > μ0 or Ha: μ > $119,155. This hypothesis holds that if the new annual average household income is found to be greater than the 2010 value of