1. **Problem Statement:** We have tip percentages for 450 meals and want to estimate the average tip percentage using random samples. 2. **Part A:** Given random IDs 16, 117, 307, 95, 170, find their tip percentages from the table and compute the sample mean. 3. **Formula for sample mean:** $$\bar{x} = \frac{1}{n} \sum_{i=1}^n x_i$$ where $x_i$ are the sample values and $n$ is the sample size. 4. **Part A Calculation:** Tips for IDs 16, 117, 307, 95, 170 are 12%, 12%, 16%, 15%, 13% respectively. 5. Compute sample mean: $$\bar{x} = \frac{12 + 12 + 16 + 15 + 13}{5} = \frac{68}{5} = 13.6\%$$ Rounded to nearest tenth: 13.6%. 6. **Part B:** The average from a sample is a **statistic** because it is computed from sample data, not the entire population. 7. **Part C:** For 15 random IDs, find their tip percentages and compute the sample mean. 8. Tips for IDs 16, 283, 271, 9, 287, 440, 192, 409, 26, 18, 17, 120, 415, 355, 149 are (from table): 12%, 17%, 13%, 10%, 9%, 11%, 11%, 13%, 10%, 15%, 16%, 13%, 12%, 10%, 11%. 9. Compute sample mean: $$\bar{x} = \frac{12 + 17 + 13 + 10 + 9 + 11 + 11 + 13 + 10 + 15 + 16 + 13 + 12 + 10 + 11}{15} = \frac{188}{15} \approx 12.5\%$$ 10. **Part D:** The larger sample mean (Part C) is more reliable for inference because it uses more data. 11. **Part E:** Reasonable inference: The average tip percentage is about 12.5%, close to the population mean 12.58%, indicating the sample is representative. 12. **Part F:** Error in Part A sample mean: $$|13.6 - 12.58| = 1.02\%$$ Rounded to nearest tenth: 1.0%. 13. **Part G:** Error in Part C sample mean: $$|12.5 - 12.58| = 0.08\%$$ Rounded to nearest tenth: 0.1%.