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Pages 2

Managerial Statistics Math 533

Project A

The following statistical information is based on Data from the AJ Davis Dept. Store, who wanted to find out a little more about their credit customers. The Data is compromised of a sample of 50 credit customers based on five different variables

The 1st individual variable is based on location divided in 3 different categories. 1) Rural-which is an area outside of cities and towns. 2) Urban-pertaining to a city or a town and 3) Suburban-a residential district located on the outskirts of a city. According to the graph you have 26% of the population lives in the Rural area, 30% lives in the Suburban area and the largest 44% lives in the Urban. To sum it up the majority of the Credit Customers leaves in the Urban locations.

The first pairing is between Size and Income. Based on the Data at hand the graph shows that the size of people’s income is less than their household size. According to the Data people’s households have higher percentages than the money they bring in to support their households.

The 2nd Individual pairing shows a graph of credit balances based on the data provided. The Median credit balance is $4,090. The data starts with $1,864 as the lowest credit balance and the highest is $5,678. The range of the Credit balances is $1638.25

In the 2nd pairing based on the data provided. People who have lived in the same location the longest have high credit balances, than the majority of those that have the lowest credit balances and shortest time living in the same location.

The 3rd pairing based on the Data provided is Location and Credit Balances. Based on the chart the highest credit balance is out of the Urban location, which tends to have a higher population, where people would normally spend more. The lowest Credit Balance comes out of the Rural location where it is considered a…...

...Natasha Douglas Managerial Statistics Math 533 Project A The following statistical information is based on Data from the AJ Davis Dept. Store, who wanted to find out a little more about their credit customers. The Data is compromised of a sample of 50 credit customers based on five different variables The 1st individual variable is based on location divided in 3 different categories. 1) Rural-which is an area outside of cities and towns. 2) Urban-pertaining to a city or a town and 3) Suburban-a residential district located on the outskirts of a city. According to the graph you have 26% of the population lives in the Rural area, 30% lives in the Suburban area and the largest 44% lives in the Urban. To sum it up the majority of the Credit Customers leaves in the Urban locations. The first pairing is between Size and Income. Based on the Data at hand the graph shows that the size of people’s income is less than their household size. According to the Data people’s households have higher percentages than the money they bring in to support their households. The 2nd Individual pairing shows a graph of credit balances based on the data provided. The Median credit balance is $4,090. The data starts with $1,864 as the lowest credit balance and the highest is $5,678. The range of the Credit balances is $1638.25 In the 2nd pairing based on the data provided. People who have lived in the same location the longest have high credit balances, than the majority of those...

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...Project Part B: 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 is Ha: µ > 50000, the given test is a one-tailed z-test. Critical Value and Decision Rule: The critical value for significance level, α=0.05 for a lower-tailed z-test is given as-1.645. Decision Rule: Reject H₀, if z – statistic, -1.645 Test Statistic - minitab One-Sample Z: Income ($1000) Test of mu = 50 vs < 50 The assumed standard deviation = 14.55 95% Upper Variable N Mean StDev SE Mean Bound Z P Income ($1000) 50 43.48 14.55 2.06 46.86 -3.17 0.001 Interpretation of Results and Conclusion: Since the P-value (0.0001) is smaller than the significance level (0.05), we reject the null hypothesis. The p-value implies the probability of rejecting a true null hypothesis. The significance level of 0.05, there is enough evidence to support the claim that the average annual income was less than $50,000. Confidence Interval - minitab One-Sample Z The assumed standard deviation = 14.55 N Mean SE Mean 95% CI 50 43.48 2.06 (39.45, 47.51) The 95% upper confidence limit...

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...Project Part B: Hypothesis Testing and Confidence Intervals | | Your manager 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. 1. Using the sample data, perform the hypothesis test for each of the above situations in order to see if there is evidence to support your manager’s belief in each case a.-d. In each case use the Seven Elements of a Test of Hypothesis, in Section 6.2 of your text book with α = .05, and explain your conclusion in simple terms. Also be sure to compute the p-value and interpret. 2. Follow this up with computing 95% confidence intervals for each of the variables described in a.-d., and again interpreting these intervals. 3. Write a report to your manager about the results, distilling down the results in a way that would be understandable to someone who does not know statistics. Clear explanations and interpretations are critical. Project Part B: 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 >...

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...Course Project A – AJ Davis Department Store Keller Graduate School In reviewing the data for AJ Davis Department Store, the below diagrams represents the detailed statistical analysis of the data collected from a sample of 50 credit consumers. The data collected was based on the following five variables: location, income, size, years and credit balances. The first individual variable considered was Location. The three subcategories are Rural, Suburban, and Urban. Shown below is the frequency distribution and pie chart, the maximum number of customer belonging to the Urban category were 42%, followed by the Suburban of 30% and Rural at 28%. Since this is a categorical variable, the measure of central tendency and descriptive statistics was not calculated. Frequency Distribution Location Frequency Rural 14 Suburban 15 Urban 21 The second variable is Credit Balances, displayed in the histogram below in the frequency of how many consumers and their credit balances at department store. Descriptive Statistics: Credit Balances ($) Variable N N* Mean SE Mean StDev Minimum Q1 Median Q3 Credit Balance ($) 50 6 3964 132 933 1864 3109 4090 4748 Variable...

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...1) Mean: The mean of a set of numbers is the average. The mean is calculated by finding the sum of all the values and dividing by the number of values. 11+12+12+13+14+16+18+19+20 = 135 There are 9 numbers in the series, so the mean is: Mean = 135/9 = 15 Median: The median of a series of numbers is the number that appears in the middle of the list when arranged from smallest to largest. For a list with an odd number of members, the way to find the middle number is to take the number of members and add one. Then divide that value by two. In our case, there are 9 numbers in the series. 9+1 = 10 and half of 10 is 5. The fifth number in the series is the median or 14. If the number of members of the series was even, the average of the two middle numbers would be the median. Mode: The mode is the number in the series that appears the most often. If there is no single number that appears more than any other number in the series, there is no value for the mode. The number 12 appears twice in the series. The mode of this series is 12. Quintile: The first quartile of a group of values is the value such the 25% of the values fall at or below this value. The third quartile of a group of values is the value such that 75% of the values fall at or below this value. The first quartile may be approximately calculated by placing a group of values in ascending order and determining the median of the values below the true median, and the third quartile is approximately calculated by...

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...Maurice S. Butler Math533—Applied Managerial Statistics Course Project: Part A Introduction This project is based upon statistical data compiled concerning AJ Davis Department Stores, specific to a sample of its customer base. It is with intent of establishing relationship between location, gross income, and credit balances carried by customers that the following statistical analysis has been performed. It is assumed that information obtained as well as the interpretation of statistical analysis will enable credible recommendations in regard to future revenues or continued handling and/or maintenance of its receivables. Variables The first variable is the gross income of the stores’ customers. The data set includes 50 customers with gross income ranging from $20,000 to $79,000 per year. Compilation of the data into a frequency/relative frequency table (see below) reveals that the greatest frequency and relative frequency of the store’s customers is found within the $30,000 to $49,000 range. Fifty-two percent of the store’s customer base gross income is found within this range. First and third quartiles have been calculated to be 33 and 57 respectfully. However, no outliers have been identified within the data set. Income ($1000) | Frequency | Relative Frequency | 20-29 | 5 | 10% | 30-39 | 13 | 26% | 40-49 | 13 | 26% | 50-59 | 8 | 16% | 60-69 | 9 | 18% | 70-79 | 2 | 4% | | 50 | 100% | My second variable is the outstanding credit balances...

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