How can the lessons from "Cracking the PM Interview" be applied in a real-world product management scenario?

Yes, there are several companies where Product Managers have successfully implemented the practice of making minor product changes and gathering data independently. For instance, at Facebook, Product Managers often run A/B tests for minor changes in the product and gather data to analyze the impact. Similarly, at Amazon, Product Managers are known to make minor tweaks to the product features or pricing and independently gather and analyze data to understand customer response. This practice is quite common in tech companies with a strong culture of data-driven decision making.

Real-world scenarios where a Product Manager's ability to form a working relationship with engineers can be crucial include:

1. Product Development: A PM needs to work closely with engineers to understand the feasibility of product features and to ensure that the product is developed as per the defined specifications.

2. Prioritization: PMs often have to make decisions about feature prioritization. Understanding the complexity and time required for engineering tasks can help in making informed decisions.

3. Problem Solving: When issues arise during the development process, a good working relationship can facilitate effective problem-solving and decision-making.

4. Innovation: Collaborative relationships can lead to innovative solutions, as engineers can provide valuable technical insights.