STATISTICS PROBLEM

Statistics Problem

Statistics Problem

Armed Forces Credit Union would requires a funding fee, which varies from 0 to 3.3% of the loan amount, depending on the number of times you have obtained a VA loan. The fee is reduced if you choose to put money down. The borrower has the option to finance the funding fee into the loan amount. The funding fee helps offset the cost to administer the VA Loan program. To determine your VA funding fee, reference the chart below:

Type of Veteran

DownPayment

First TimeUse

Subsequent Use for Loans to9/30/2011

Regular Military

None5% or more10% or more

2.15%1.50%1.25%

3.30%1.50%1.25%

Reserves/NationalGuard

None5% or more10% or more

2,40%1.75%1.50%

3.30%1.75%1.50%

The following persons are exempt from paying the funding fee:

Veterans receiving VA compensation for service-connected disabilities.

Veterans who would be entitled to receive compensation for service-connected disabilities if they did not receive retirement pay.

Surviving spouses of veterans who died in service or from service-connected disabilities (whether or not such surviving spouses are veterans with their own entitlement and whether or not they are using their own entitlement on the loan).

Population assumptions

1. All of the treatment populations are normally distributed. Although we do not know if the populations are normally distributed, we can trust to the robustness of the F statistic as long as the populations are relatively symmetrical.

2. All of the treatment populations have the same variance, s2. If the sample sizes are all the same (as they must be for the procedures described in Step 5) and if the treatment sample variances are approximately equal, then we can trust to the robustness of F to meet this assumption. Examination of the data indicates that the sample variances are all comparable.

Sampling assumptions

1. The samples (one for each treatment) are independent of one another. Computational procedures for the dependent-sample ANOVA and the mixed-sample ANOVA are more complicated; an advanced text should be consulted for those procedures.

2. Each sample is obtained by independent (within-sample) random sampling (or random assignment and the assumption of randomness of biological systems is made).

3. Each sample has at least two observations, and all of the samples have the same number of observations. Consult an advanced statistics text for procedures for analyzing factorial experiments with differing numbers of observations in each treatment.

The sampling assumptions are met for this example: because different (unrelated) volunteers were assigned to each treatment, the samples are independent of one another; random assignment was used; and there are an equal number of observations ...