The ARC Leasing Co. leases both trucks and autos. You have decided to test the client’s assertion that the average combined useful life for all leases is 35 months.

The client has 12,000 auto leases and 2,000 truck leases. You believe that the truck leases have a different variability from the auto leases and therefore decide to use stratified sampling. You decide on a confidence level of 95%. You desire a precision of + 1.5 months; thus, in determining sample size, you use 21,000 lease months as the total precision for the population.

You select a pilot sample of 50 auto leases and 50 truck leases, with the following results:

Required :

a. Calculate the required sample size.

b. Assume that the sample, including the pilot sample of 100, yielded the following results (using the sample size calculated in a above):

The sample size was divided evenly between the strata. Calculate an appropriate interval estimation at the desired confidence level for the life of the leases.

c. Evaluate, using an appropriate decision rule, the client’s assertion that the combined useful life for all leases is 35 months.

Transcribed Image Text:

Population size Sample Sample size mean Sample std. dev. Auto leases 12,000 50 32 months 10.1 Truck leases 2,000 50 38 months 16.2 14,000 100