Brief Introduction
AJ Davis is one of the department stores which have many credit customers. The store has decided to find out more information about its credit customers. There are 50 credit customers who were selected for the data collection on five variables such as location, income, size, years, and credit balance. In order to understand more about their customer, AJ DAVIS must used graphical, numerical summary to be able to interpret and better expand their business in the future.

A. Discuss your 1st individual variable, using graphical, numerical summary and interpretation:
A histogram shows the distribution of data within the income generated from 20-60. In this Histogram graph of Income, it shows that the graph is not symmetrical. The graph shows that this graph is more like two graph because there is a clear difference between income generating from 20-40 and from 50-above. There are two separated cluster; therefore, the skewness of this graph is skewed right. Income has a lower value of kurtosis which indicates a lower, less distinct peak. The following table shows the numerical summary of Income:

B. Discuss your 2nd individual variable, using graphical, numerical summary and interpretation :

A histogram shows the distribution of data within the Credit Balance. In this Histogram graph of Credit Balance, it shows that the graph is symmetrical with the exception of one outlier which is credit balance of $2,000. This is a normal distribution with a single peak at the center of the distribution. By symmetric, I mean that the distribution can be folded about an axis and the two sides almost coincide. The following table shows the numerical summary of Credit Balance:

The P-value of the Credit Balance using the Anderson-Darling Normality Test is 0.400 and the A-Squared is 0.38. With the 95% Confidence Interval for Mean, Median, and St Dev are as followed:

This graph show that the number of the customers current credit card...

...Article Review 1
DeGeorge, B., Santoro, A. (2004). “Manipulatives: A Hands-On Approach to Math.” Principal, 84 (2), (28-28).
This article speaks about the importance and significance of the use of manipulatives in the classroom, specifically in the subject of math. Manipulatives have proven to be valuable when used in a math class and are even more valuable to the children when they are young, and are learning new math concepts. Students are able to physically visualize the math concepts and gain knowledge because they understand what they’re learning a whole lot better and they also are able to gain insights on those concepts. Different examples of manipulatives may include counting with beans or M&M’s, using pattern blocks, puzzles, tangrams, and flash cards, just to name a few.
Using manipulatives in a math class are beneficial to both the student and the teacher because the teacher is able to explain the concepts to the students in a much easier manner using the hands-on technique, rather than explaining it verbally. It’s especially beneficial to the student because by incorporating these manipulatives into their learning process, they are able to pick up the concepts much quicker and in a way that they better understand, yet are having fun while doing it. When they have the concepts down, the students’ self-esteem goes up and they feel encouraged to keep on going.
After...

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PROJECT PART C: Regression and Correlation Analysis
Math-533 Applied Managerial Statistics
Prof. Jeffrey Frakes
December 12, 2014
Jared D Stock
1. Generate a scatterplot for income ($1,000) versus credit balance ($), including the graph of the best fit line. Interpret.
This scatter plot graph is a representation of combining income and credit balance. It shows the income increasing as the credit balance increases. As a result of this data it can be inferred that there is a positive relationship between the two variables. Because of the positive relationship between income and credit balance the best fit line or linear regression line fits the data quite well. The speculation can be strongly made that the customer with the largest income will, more than likely, have the largest credit balance.
2. Determine the equation of the best fit line, which describes the relationship between income and credit balance.
Regression Analysis: Income($1000) versus Credit Balance($)
The regression equation is
Income($1000) = - 3.52 + 0.0119 Credit Balance($)
Predictor Coef SE Coef T P
Constant -3.516 5.483 -0.64 0.524
Credit Balance($) 0.011926 0.001289 9.25 0.000
S = 8.40667 R-Sq = 64.1% R-Sq(adj) = 63.3%
Analysis of Variance
Source DF SS MS F P
Regression 1 6052.7 6052.7 85.65 0.000
Residual Error 48 3392.3 70.7...

...A P P E N D I X E S
Tables and Data Sets
A Areas under the Normal Curve B Student’s t Distribution C Data Set 1 — Real Estate D Data Set 2 — Major League Baseball E Data Set 3 — OECD F Data Set 4 — Northwest Ohio School Districts G Critical Values of the F Distribution H Critical Values of Chi-Square I Binomial Probability Distribution J Factors for Control Charts K Poisson Distribution L Table of Random Numbers M Wilcoxon T Values N Banking Data Set — Case
262 Appendixes
Appendix A
Areas under the Normal Curve
Example: If z = 1.96, then P(0 to z) = 0.4750 z
z
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 0.00 0.0000 0.0398 0.0793 0.1179 0.1554 0.1915 0.2257 0.2580 0.2881 0.3159 0.3413 0.3643 0.3849 0.4032 0.4192 0.4332 0.4452 0.4554 0.4641 0.4713 0.4772 0.4821 0.4861 0.4893 0.4918 0.4938 0.4953 0.4965 0.4974 0.4981 0.4987 0.01 0.0040 0.0438 0.0832 0.1217 0.1591 0.1950 0.2291 0.2611 0.2910 0.3186 0.3438 0.3665 0.3869 0.4049 0.4207 0.4345 0.4463 0.4564 0.4649 0.4719 0.4778 0.4826 0.4864 0.4896 0.4920 0.4940 0.4955 0.4966 0.4975 0.4982 0.4987
0.4750 0
0.02 0.0080 0.0478 0.0871 0.1255 0.1628 0.1985 0.2324 0.2642 0.2939 0.3212 0.3461 0.3686 0.3888 0.4066 0.4222 0.4357 0.4474 0.4573 0.4656 0.4726 0.4783 0.4830 0.4868 0.4898 0.4922 0.4941 0.4956 0.4967 0.4976 0.4982 0.4987
1.96
0.03 0.0120 0.0517 0.0910 0.1293 0.1664 0.2019 0.2357 0.2673 0.2967 0.3238 0.3485 0.3708 0.3907 0.4082...

...Brief Introduction:
AJ Davis is a department store chain, which has many credit customers and want to find out more information about these customers. AJ Davis has complied a sample of 50 credit customers with data selected in the following variables: Location, Income (in $1,000’s), Size (Number of people living in the household), Years (number of years the customer has lived in the current location), and Credit Balance (customers current credit card balance on the store’s credit car, in $).
The manager at AJ Davis has speculated 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 exceeds 40%
c. The average (mean) number of years lived in the current home is less than 13 years
d. The average (mean) credit balance for suburban customers is more than $4300
I will analyze the speculated data listed above by performing hypothesis test for each of the above situations (using the Seven elements of a Test Hypothesis with a=.05) in order to see if there is evidence to support my manager’s beliefs in each case (a-d), explain my conclusion in simple terms, compute the p-value with the interpretation, follow up with computing 95% confidence intervals for each of the variables described in a. to d. along with interpreting these intervals. This paper will also include an Appendix with all the steps in hypothesis testing, as well as the confidence intervals and...

...Statistical Report
The Relationships between Location, Income, and Credit Balance for the customers of AJ Davis Department Store
Math533
Course Project Part A
AJ DAVIS DEPARTMENT STORES
AJ Davis Department Store Customer Research
A. Brief Introduction
The department store AJ Davis would like to find out more information about their customers. A sample of 50 credit customers is selected with data collected on the following five variables:
1. LOCATION (Rural, Urban, Suburban)
2. INCOME (in $1,000's – be careful with this)
3. SIZE (Household Size, meaning number of people living in the household)
4. YEARS (the number of years that the customer has lived in the current location)
5. CREDIT BALANCE (the customers current credit card balance on the store's credit card, in $).
This report presents the findings of three individual variables extensively which include location, income, and credit balance. We will also discuss three pairing of variables extensively which include: location and income, income and credit balance, as well as location and credit balance. These variables and pairings will give AJ Davis the most information about their customers.
B. 1st Individual Variable is location:
Location is very important to AJ Davis because knowing where your customers come from is the basis for most of your research. From location you can draw a correlation with every variable.
Interpretation: From the pie chart...

...The below report presents the detailed statistical analysis of the data collected from a sample of credit customers in the department store “AJ DAVIS Departmental stores”.
The 1st individual variable considered is Location. It is a category variable. The three subcategories are Urban, Suburban and Rural. Category variable, the measures of central tendency and descriptive statistics has not been calculated for this variable. The frequency distribution and pie chart are below:
|Frequency Distribution: |
|Location |Frequency |
|Urban |21 |
|Suburban |15 |
|Rural |14 |
[pic]
From the frequency distribution and pie chart, it is display the maximum number of customers belongs to the rural category (42%), suburban category (30%) and Only 28% of the customers belong to the urban category.
The 2nd individual variable considered is Size. It is a quantitative variable. The measures of central tendency, variation and other descriptive statistics have been calculated for this variable are below:
|Descriptive Statistics: |
|Size |
|Mean |3.42 |
|Median |3 |
|Mode |2 |
|Standard Deviation...

...August 26, 2012
MATH533
Course Project Part C
Professor Khago
Introduction:
The following report displays regression and correlation analysis for AJ Davis Department Stores data on credit balance and size. We will use the data collected from 50 credit customers to complete the following analysis;
* Generate a scatterplot for CREDIT BALANCE vs. SIZE, including the graph of the "best fit" line. Interpret.
* Determine the equation of the "best fit" line, which describes the relationship between CREDIT BALANCE and SIZE.
* Determine the coefficient of correlation. Interpret.
* Determine the coefficient of determination. Interpret.
* Test the utility of this regression model (use a two tail test with α =.05). Interpret your results, including the p-value.
* Based on your findings in 1-5, what is your opinion about using SIZE to predict CREDIT BALANCE? Explain.
* Compute the 95% confidence interval for. Interpret this interval.
* Using an interval, estimate the average credit balance for customers that have household size of 5. Interpret this interval.
* Using an interval, predict the credit balance for a customer that has a household size of 5. Interpret this interval.
* What can we say about the credit balance for a customer that has a household size of 10? Explain your answer.
* Using MINITAB run the multiple regression analysis using the variables INCOME, SIZE and YEARS to predict CREDIT...

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PROJECT PART B: Hypothesis Testing and Confidence Intervals
Math-533 Applied Managerial Statistics
Prof. Jeffrey Frakes
December 8, 2014
Jared D Stock
A.) The average (mean) annual income was greater than $45,000
Null Hypothesis: The average (mean) annual income is greater than or equal to $45,000.
Ho: u > $45,000
Alternative Hypothesis: The average (mean) annual income was less than $45,000
Ha: u < $45,000
I will use a = .05 as the significance level, and observing the sample size of n < 30 which tells me I need to use a Z-Test to find the mean of this test and the hypothesis. As the alternative hypothesis is Ha: u < $45,000, the given test is a one-tailed Z-Test.
The critical value for the significance level, α=0.05 for a one-tailed z-test is -1.645.
Decision Rule: We must reject the hypothesis if z >1.645
Test Statistics from Minitab:
One-Sample Z: Income ($1000)
Test of mean = 45, < 45
The proposed standard deviation = 14.64
95% Upper
Variable N Mean StDev SE Mean Bound Z P
Income ($1000) 50 43.48 14.55 2.06 46.86 0.49 0.311
Confidence Intervals from MiniTab:
One-Sample Z
The assumed standard deviation = 14.64
N Mean SE Mean 95% CI
50 42.61 2.06 (39.45, 47.51)
Summary
Since the...