Question

The Penn National Bank (PNB) has 500,000 users of credit cards throughout the state of PA. In order to apply for a credit card, one must provide his or her name, address, phone number, income, and education. The bank is interested in determining whether there is a relationship between the way the card is used and the socioeconomic characteristics of the user. For example, is there any difference between consumers who use the card for major purchases (like appliances) and those that use it for minor ones? Is the research design and technique appropriate in this case? If yes, why? If no, why not?

a) Identify the sampling frame that PNB should use.

b) How would you draw a simple random sample from the sampling frame identified in part a.

c) How would you draw a stratified sample from the sampling frame?

d) Which method would you prefer? Why?

Answer 1

The research design and technique is appropriate in this case because, we have to choose randomly sample from the population.Here population is list of all customers and sample we have to choose by "Simple Random Sampling Without Replacement".

A) Sampling Frame :A list of the items or people forming a population from which a sample is taken. Therefore by considering defination of sampling frame, a list containing all 500,000 users of credit cards forms a samplilng frame for this experiment.

B) To draw a simple random sample from the population we have to follow following steps. 1) List all 500,000 users giving them serial numbers. 2) By using any statistical software or simply using Ms-Excel you have to draw random numbers by giving appropriate numbers. Keep in mind that as you increases nmber of customers your experimental precision increases but your experimental cost also increases. 3) After you get random numbers, then drom the users from the list which we have created in step 1. 4) After choosing study further.

c) Stratified Sampling : Stratified random sampling is a method of sampling that involves the division of a population into smaller groups known as strata. In stratified random sampling, orstratification, the strata are formed based on members' shared attributes or characteristics.

By considering above defination we can stratify whole population using different attributes such as example given by you {consumers who use the card for major purchases (like appliances) and those that use it for minor ones} you can statify population into two sratas as a & b.(a)customers using the card for manor purchases (b) customers using the card for minor purchases. Or By taking their account balance or gender in consideration we can stratify population.

D) Example given by you ,I suggest that you have to use stratified sampling by creating appropriate stratas.