Aj Davis Department Stores
AJ Davis Department Stores - 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 Davis Department stores is on average $3970.00. Based on the graph, 18 of the 50 sampled fall below and 17 fell above the average. The standard deviation for credit balance is 931.9.
Income
Annual Income of Davis Department Stores customers range anywhere from $22,000 to $67,000. Majority of their customers have an annual income of about $43,740. The standard deviation for income is $14,640.
Size
Average household size is about 3.4. Based on the graph above, 15 of the 50 sampled have a household size of 2 (the most common household size). The standard deviation is 1.739.
Credit Balance and Location
Comparing income to credit balance shows the higher the income the higher the credit balance. Although a few of the sampled customers have a low income and a high balance this is not a normal scenario based on the graph above.
Years and Credit Balance
Location and Size
Based on the graph, it is clear that the household size is normally 2. Urban and Rural areas seem to have the most households with 2 whereas the suburban location has more households with 3 members.
Total Calculations
The data as a whole has the following calculations: | Income ($1000) | Size | Years | Credit Balance ($) | Average | 43.74 | 3.42 | 12.26 | 3970.46 | Std Dev | 14.64 | 1.74 | 5.09 | 931.9 | Median | 43 | 3 | 13 | 4090 |
Project Part B - Hypothesis Testing and Confidence Intervals a. The average annual income was less than $50,000
Ho: m >= 50000
Ha: m<50000
Level of Significance: 0.05
Rejection region: Z< -1.645 z = (43.70 – 50)/(14.6396/sqrt(50)) = -3.024 z falls in the rejection region so reject Ho there is sufficient evidence at the 0.05 level of significance.
P = .5 - .4987 = .0013
Stacie Borowicz
June 14, 2013
Math 533
Project Part A – Exploratory Data Analysis
Credit Balance ($)
Based on a sample of 50 customers, the credit balance for customers of Davis Department stores is on average $3970.00. Based on the graph, 18 of the 50 sampled fall below and 17 fell above the average. The standard deviation for credit balance is 931.9.
Income
Annual Income of Davis Department Stores customers range anywhere from $22,000 to $67,000. Majority of their customers have an annual income of about $43,740. The standard deviation for income is $14,640.
Size
Average household size is about 3.4. Based on the graph above, 15 of the 50 sampled have a household size of 2 (the most common household size). The standard deviation is 1.739.
Credit Balance and Location
Comparing income to credit balance shows the higher the income the higher the credit balance. Although a few of the sampled customers have a low income and a high balance this is not a normal scenario based on the graph above.
Years and Credit Balance
Location and Size
Based on the graph, it is clear that the household size is normally 2. Urban and Rural areas seem to have the most households with 2 whereas the suburban location has more households with 3 members.
Total Calculations
The data as a whole has the following calculations: | Income ($1000) | Size | Years | Credit Balance ($) | Average | 43.74 | 3.42 | 12.26 | 3970.46 | Std Dev | 14.64 | 1.74 | 5.09 | 931.9 | Median | 43 | 3 | 13 | 4090 |
Project Part B - Hypothesis Testing and Confidence Intervals a. The average annual income was less than $50,000
Ho: m >= 50000
Ha: m<50000
Level of Significance: 0.05
Rejection region: Z< -1.645 z = (43.70 – 50)/(14.6396/sqrt(50)) = -3.024 z falls in the rejection region so reject Ho there is sufficient evidence at the 0.05 level of significance.
P = .5 - .4987 = .0013