Final answer:
From the random sample of 200 credit card customers where 136 incurred interest charges, we can infer that approximately 68% of the store's credit card customer base may have incurred interest charges. A confidence interval could further refine this estimation to account for a margin of error.
Step-by-step explanation:
The financial manager of a large department store chain selected a random sample of 200 of its credit card customers and found that 136 had incurred an interest charge during the previous year. One statistical analysis that can be derived from this sample data is the estimation of the proportion of the entire credit card customer population that may have incurred interest charges. This is done by calculating the sample proportion, which is the number of customers who incurred an interest charge divided by the total number of sampled customers.
To calculate this for the given data:
- Divide the number of customers who incurred an interest charge (136) by the total number of customers in the sample (200).
- Multiply the result by 100 to get the percentage.
The calculation would be (136 / 200) * 100 = 68%. This means that, based on the sample, we can infer that approximately 68% of the credit card customers of the department store chain incurred interest charges in the past year. It is also important to consider the confidence interval for this sample proportion to understand the margin of error and to provide a range within which the true population proportion is likely to fall.