Final answer:
To perform circular systematic sampling from given signal data, divide the total number of days by the sample size to determine the sampling interval, use a random number to find the starting point, and then select every 4th day, continuing in a circular manner if the end of the list is reached.
Step-by-step explanation:
To select a random sample of 5 days by circular systematic sampling method from the provided data, first, we should determine the sampling interval. Since there are 22 signals sent from a station on different days, and we need a sample of 5 days, we divide 22 by 5, which gives us approximately 4. This means that we should select every 4th day for our sample.
Next, we would use a random number to determine the starting point. Suppose this random starting point is given by the random number table from the lecture and is 3. We then count every 4th day from this point. If we reach the end of the list, we continue counting from the beginning (hence 'circular').
The process would be as follows: Starting with the 3rd day (which corresponds to 10 faded out signals), we then select the 7th day (24 signals), 11th day (31 signals), 15th day (6 signals), and 19th day (4 signals) to be in our sample. If we started from a different random starting point, we would follow the same interval, but begin our count from the new starting number.