A personal trainer wants a random sample of her clients. She gets the list of all her clients from the gym manager and assigns each one a number. She then uses a table of random numbers to select 50 clients from the list.
What is your question?
Indicate which of the following sampling techniques are examples of random sampling. For those that are not examples of random sampling, explain why.
This looks like a random sample.
To select a random sample of her clients, the personal trainer follows these steps:
1. Obtain the list of all her clients from the gym manager.
2. Assign each client a unique number, starting from 1 and incrementing by 1 for each client. This step ensures that each client has a distinct identifier.
3. Refer to a table of random numbers, which is a tool used to generate a sequence of non-repeating random digits. Each digit in the table represents a unique number from 0 to 9.
4. Determine the range of random numbers needed to select the desired sample size. In this case, the personal trainer wants to select 50 clients.
5. Start at any random position in the table of random numbers.
6. Read the first digit from the table. This digit indicates the first client's number to include in the sample. If the digit exceeds the total number of clients, ignore it and move to the next digit.
7. Continue reading the subsequent digits from the table until the desired sample size is reached. Again, disregard any digits that exceed the total number of clients.
8. Record the numbers obtained from the random number table. These numbers correspond to the clients to be included in the random sample.
9. After selecting 50 clients, the personal trainer will have a representative sample from her client list.
By using this method, the personal trainer can ensure a random and unbiased selection of clients for her sample.