AJ Davis Department Store Part B
AJ Davis Department Store
Introduction
The following information will show whether or not the manager’s speculations are correct. He wants to know the following information: Is the average mean greater than $45,000? Does the true population proportion of customers who live in an urban area exceed 45%? Is the average number of years lived in the current home less than 8 years? Is the credit balance for suburban customers more than $3200? Hypothesis testing and confidence intervals for situations A-D are calculated. A. THE AVERAGE (MEAN) ANNUAL INCOME WAS LESS THAN $45,000.

Solution:
Step 1: Null Hypothesis: The average (mean) annual income was equal to $45,000. H_0: μ=45,0000
Step2: Alternate Hypothesis: The average (mean) annual was less than $50,000. H_a: μ 45 , a z-test for the mean will be used to test the given hypothesis. As for the alternative hypothesis, which is Ha:μ0.45 and the given test is a one-tailed (upper-tailed) z-test. Step 4: Critical Value and Rejection Region:

The critical value for significance level is ∝=0.05. The upper tail z-test is 1.645. Rejection Region: Reject H_0,if z-statistic>1.645.
Step 5: Assumptions:
The sample size in this experiment is n 0.4
95% Lower
Sample X N Sample p Bound Z-Value P-Value
1 21 50 0.420000 0.305190 0.29 0.386
Step 7: Interpretation:
According to the calculations, the p-value is 0.386. This value is larger than the significance level of 0.05. Therefore, we will not reject the null hypothesis. There is no sufficient evidence to support the claim that the true population proportion of customers who live in an urban area is greater than 40%. Based on the results provided by MINITAB below, the lower 95% confidence limit is 0.28. Since 0.42 is greater than the 95% lower confidence limit, hence, we cannot support the claim that the true population proportion of customers who live in an urban area is greater than 45%. Confidence Interval:

...
Course Project Part A
September 15, 2013
Applied Managerial Statistics
Professor Mayers
Brief Introduction
The following report presents a detailed statistical analysis of AJDavisDepartmentStore credit customers. Data was collected from a sample of 50 AJDavis credit customers on five variables which are Location, Size, Income, Years, and Credit Balance. Out of the five variables,...

...AJDavisDepartmentStore
Project PartB: Hypothesis Testing and Confidence Intervals
A. The average (mean) annual income was less than $50,000
• Null Hypothesis is the average annual income is ≥ to $50,000.
o Ho: µ ≥ 50,000
• Alternate Hypothesis is the average annual income is < than $50,000.
o Ha: µ < 50,000
• Analysis Plan significance level is: a = 0.05...

...INTRODUCTION
Base on the data collected in the previous samples, the manager has made an alternative hypothesis on the following:
A) The average (mean) annual income was less than $50,000
B) The true population proportion of customers who live in an urban area exceed 40%
C) The avarage (mean) number of years lived in the current home is less than 13 years D) The avarage (mean) credit balance for suburban costumers is more than $4,300
Using the sample data, we...

...AJDavisDepartmentStores - Project Part A, B, and C
Stacie Borowicz
June 14, 2013
Math 533
Project Part A – Exploratory Data Analysis
Credit Balance ($)
Based on a sample of 50 customers, the credit balance for customers of DavisDepartmentstores is on average $3970.00. Based on the graph, 18 of the 50 sampled fall below and 17 fell above...

...Problem N°1
1.Formulate the null and alternative hypotheses.
Null Hypothesis: The average (mean) annual income was greater than or equal to $50,000
H_0: μ≥50000
Alternate Hypothesis: The average (mean) annual income was less than $50,000.
H_a: μ 30 we will use the z-test.
As Ha:μ0.40 the, test is a right tailed z-test.
The critical value for significance level, α=0.05 for a right tailed z-test is given in the table as: 1.645.
Decision Rule: Reject H_0,if z>1.645
3. Calculate the...

...The following report presents a detailed statistical analysis of AJDAVISdepartmentstore customers. Data was collected from a sample of 50 AJDAVIS credit customers for the purpose of learning more about the customers of AJDAVIS.
The first variable considered is Location, a categorical variable. The three subcategories are Urban, Suburban and Rural. The frequency distribution...

...The following report presents the detailed statistical analysis of the data collected from a sample of credit customers in the department chain storeAJDAVIS.
The 1st individual variable considered is Location. It is a qualitative variable. The three subcategories are Urban, Suburban and Rural. Since this is a qualitative variable, the measures of central tendency and descriptive statistics has not been computed for this variable. The...

...Project PartB: Hypothesis Testing and Confidence Intervals
a. The average (mean) annual income was less than $50,000
Null Hypothesis: The average annual income was greater than or equal to $50,000
H₀: µ > 50000
Alternate Hypothesis: The average annual income was less than $50,000.
Ha: µ > 50000
Analysis Plan: Significance Level, α=0.05.
Since the sample size, n > 30 I will use z-test for mean to test the given hypothesis.
As the alternative hypothesis...

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