As part of a marketing​ experiment, a department store regularly mailed discount coupons to 25 of its credit card holders. Their total credit card purchases over the next three months were compared to the credit card purchases over the next three months for 25 credit card holders who were not sent discount coupons. Determine whether the samples are dependent or independent.
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Part 1
dependent
independent

To determine whether the samples in this marketing experiment are dependent or independent, we need to examine the relationship between the two groups being compared: 

1. **Group 1:** 25 credit card holders who received discount coupons.
2. **Group 2:** 25 credit card holders who did not receive discount coupons.

### Dependent vs. Independent Samples

- **Dependent Samples:** These occur when the data points in one sample are related to or paired with data points in the other sample. A common example is a before-and-after study, where the same subjects are measured at two different times.

- **Independent Samples:** These occur when the data points in one sample have no relation or pairing with the data points in the other sample. Each sample is collected independently of the other.

### Analysis

In this experiment:

- **Independent Samples**: The two groups are composed of different credit card holders. There is no indication that the purchases of those who received coupons are paired or matched in any way with those who did not. The samples are simply comparing the total purchases of one group against another, with no inherent pairing or matching. Thus, these are independent samples.

- **Dependent Samples**: If the same credit card holders had been measured twice (once with coupons and once without), the samples would be dependent. However, this is not the case here.

### Conclusion

The samples in this experiment are **independent** because each group consists of different individuals, and there is no pairing or direct relationship between the members of the two groups. The purchases of one group do not influence or correspond directly to the purchases of the other group.

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Would you like further details on how to conduct a statistical test for independent samples, or do you have any other questions? Here are some related questions to consider:

1. How do you determine if samples are dependent in other contexts?
2. What are the implications of using independent samples for statistical analysis?
3. What statistical test is appropriate for comparing independent samples?
4. How do you ensure randomness when selecting independent samples?
5. Can you give examples of when dependent samples might be used in experiments?
6. What are some potential biases that could affect independent sample comparisons?
7. How does sample size affect the reliability of independent sample comparisons?
8. How can you visualize the difference between independent and dependent samples in data analysis?

**Tip:** When dealing with independent samples, it's important to ensure that both groups are selected randomly to avoid any bias that could skew the results.

Understand the difference between dependent and independent samples in statistical analysis. Learn how to determine if samples are dependent or independent using a practical marketing experiment example. Explore the implications of using independent samples for statistical tests.

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