Questions: (b) A bank analyst wants to ask customers who have a mortgage with the bank about the customers' home-buying experiences. Which of the following best describes a random sample of customers? The analyst uses a computer program to draw 54 customers at random and selects these customers. Every set of 54 customers is equally likely to be drawn by the computer program. The analyst spends a day calling mortgage customers and selects the first 54 customers who answer because these customers are easily accessible. The analyst forms 6 groups of customers based on the customers' mortgage amounts. Then, she selects 9 customers at random from each group.

Solution Steps

A random sample is a subset of a population where each member of the population has an equal chance of being selected. This ensures that the sample is unbiased and representative of the entire population.

The first option states that the analyst uses a computer program to draw 54 customers at random, and every set of 54 customers is equally likely to be drawn. This method ensures that each customer has an equal probability of being selected, which aligns with the definition of a random sample.

The second option describes the analyst selecting the first 54 customers who answer the phone because they are easily accessible. This method introduces bias, as it does not give every customer an equal chance of being selected. Customers who are more likely to answer the phone may not be representative of the entire population.

The third option involves the analyst forming 6 groups based on mortgage amounts and then selecting 9 customers at random from each group. This method is a form of stratified random sampling, where the population is divided into subgroups (strata) and random samples are taken from each subgroup. While this method ensures representation from each subgroup, it is not a simple random sample because not every customer has an equal chance of being selected across the entire population.

Final Answer