Homework 4 A salesperson obtained a systematic sample of size 20 from a list of 500 clients. To do so, he randomly selected a number from 1 to 25 , obtaining the number 18 . He included in the sample the 18 th client on the list and every 25 th client thereafter. List the numbers that correspond to the 20 clients selected.

To determine the 20 clients selected using systematic sampling, follow these steps: 1. **Total Clients (N):** 500 2. **Sample Size (n):** 20 3. **Sampling Interval (k):** \( k = \frac{N}{n} = \frac{500}{20} = 25 \) 4. **Starting Point:** The salesperson randomly selected the number **18**. This means the first client in the sample is the 18th client on the list. 5. **Selection Process:** Starting from the 18th client, every 25th client thereafter is selected. - **1st Client:** 18 - **2nd Client:** \( 18 + 25 = 43 \) - **3rd Client:** \( 43 + 25 = 68 \) - **4th Client:** \( 68 + 25 = 93 \) - **5th Client:** \( 93 + 25 = 118 \) - **6th Client:** \( 118 + 25 = 143 \) - **7th Client:** \( 143 + 25 = 168 \) - **8th Client:** \( 168 + 25 = 193 \) - **9th Client:** \( 193 + 25 = 218 \) - **10th Client:** \( 218 + 25 = 243 \) - **11th Client:** \( 243 + 25 = 268 \) - **12th Client:** \( 268 + 25 = 293 \) - **13th Client:** \( 293 + 25 = 318 \) - **14th Client:** \( 318 + 25 = 343 \) - **15th Client:** \( 343 + 25 = 368 \) - **16th Client:** \( 368 + 25 = 393 \) - **17th Client:** \( 393 + 25 = 418 \) - **18th Client:** \( 418 + 25 = 443 \) - **19th Client:** \( 443 + 25 = 468 \) - **20th Client:** \( 468 + 25 = 493 \) 6. **Final List of Selected Clients:** \[ 18, \ 43, \ 68, \ 93, \ 118, \ 143, \ 168, \ 193, \ 218, \ 243, \ 268, \ 293, \ 318, \ 343, \ 368, \ 393, \ 418, \ 443, \ 468, \ 493 \] **Selected Client Numbers:** 18, 43, 68, 93, 118, 143, 168, 193, 218, 243, 268, 293, 318, 343, 368, 393, 418, 443, 468, 493