# Aj Davis Department Stores

**Topics:**Regression analysis, Prediction interval, Statistics

**Pages:**6 (1213 words)

**Published:**July 28, 2013

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 which is < 0.05 so do not reject Ho. 95% CI = 43.70 +- 1.96(2.0704) = (39.642 , 47.758)

We can be 95% confident that the average income lies within the confidence interval.

b. The true population proportion of customers who live in an urban area exceeds 40% c. The average number of years lived in the current home is less than 13 years Ho: m = 13

Ha: m < 13

Level of Significance: 0.05

Rejection region: Z< -1.645

z = (12.26 – 13)/(5.0862/sqrt(50)) = -1.0288

z does not fall in the rejection region so do not reject Ho there is insufficient evidence at the 0.05 level of significance. P = .5 - .3485 = .1515 which is > 0.05 so reject Ho.

95% CI = 12.26 +- 1.96(0.7193) = (10.850 , 13.67)

We can be 95% confident that the average years lived in the current home lies within the confidence interval.

d. The average credit balance for suburban customers is more than $4300 Ho: m < 4300

Ha: m > 4300

Level of Significance: 0.05

Rejection region: Z > 1.645

z = (3970.46 – 4300)/(931.8958/sqrt(50)) = -2.500

z does not fall in the rejection region so do not reject Ho there is insufficient evidence at the 0.05 level of significance. P = .5 + .4938 = .9938 which is > 0.05 so reject Ho.

95% CI = 3970.46 +- 1.96(131.79) = (3712.15 , 4228.77)

We can be 95% confident that the average credit balance for suburban customers lies within the confidence interval. Project Part C – Regression and Correlation Analysis

1.

2. Best fit line: $2591 + 403.2x

3. Coefficient of Correlation: 56.62 = 57% (Appendix A)

4. Coefficient of Determination: 55.17 = 58% (Appendix A)

5. p-value = 0.000 (Appendix A)

6. Based on this information, as the household size increases so does the credit balance. This is illustrated perfectly by the graph above. 7.

8. Confidence Interval for household size of 5 is (4368.20, 4846.90). The mean credit balance for a household size of 5, lies within this interval. (Appendix B) 9. Prediction Interval for a household size...

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