In the following paragraphs I have prepared my results of the mean average income, population of urban customers to total customers, number of years customers have lived in their current homes, and average customers credit balance.
The first variable I will discuss is the likelihood the average income is less than $50,000. After looking at the sample of the customers I have discovered that the average annual income falls between $39,680 and $47,800. When it was tested further we have strong evidence that the average income for all customers is less than $50,000.
The second variable I will discuss is the whether the percentage of urban customers is more than 40%. Initial testing revealed that the percentage of urban customers falls between 30 and 57%. Further testing revealed that we have strong evidence that the percentage of urban customers is greater than 40%.
The third variable to be discussed is whether the average years a customer has lived at their current residence is less than 13 years. The mean years a customer has lived at their current residence is between 11 and 14 years. Based on some further testing there is strong evidence that the average number of years is more than 13 years.
The fourth and final variable to be discussed is whether the average credit balance for customers is more than $4,300. The average credit balance for customers is between $3,712 and $4,228. Based on the averages we have strong evidence that the average credit balance is not more than $4,300 but actually less than $4,300.
Based on the manager predictions we can confirm that three of his four predictions are correct. The only prediction that we could not confirm was if the number of years a customer has lived at their current residence is less than 13 years. Attached to this report is an appendix which shows the results of our testing.
Annual Income (In thousands): | | | | Ho: | m=50 | Ha: | m<50 | Sample mean: | 43.74 | Sample SD: | 14.63963 | SE MEAN: | 2.070356 | | | 95% Confidence Interval: | | Lower Limit: | 39.68218 | Upper Limit: | 47.79782 | | | => 95% Confidence Interval is: [39.68, 47.80] | | | Hypothesis Test;  = .05 | | | | z = | -3.02363 | CV = -z.05 = | -1.64485 | p = | 0.001249 |

40% Population Proportion:
Ho: m = .40
Ha: m >.40
Test and CI for One Proportion

Sample X N Sample p 95% CI
1 22 50 0.440000 (0.302411, 0.577589)

Using the normal approximation.

Years: Years | | | | Ho | m=13 | Ha | m<13 | Sample mean: | 12.26 | Sample SD: | 5.086236 | SE MEAN: | 0.719302 | | | 95% Confidence Interval: | | Lower Limit: | 10.85019 | Upper Limit: | 13.66981 | | | => 95% Confidence Interval is: [10.85, 13.67] | | | | Hypothesis Test;  = .05 | | | | z = | -52.4675 | CV = -z.05 = | -1.64485 | p = | 0 |

Average Credit Balance: Credit Balance | | | | Ho | m=4300 | Ha | m>4300 | Sample mean: | 3970.46 | Sample SD: | 931.8958 | SE MEAN: | 131.79 | | | 95% Confidence Interval: | | Lower Limit: | 3712.156 | Upper Limit: | 4228.764 | | | => 95% Confidence Interval is: [3712.16, 4228.76] | | | | Hypothesis Test;  = .05 | | | | z = | 29.74779 | CV = -z.05 = | -1.64485 | p = | 1 |