Question

1. Approximately 52% of U.S. households own at least one dog. Using the random digit table provided below, explain how you would conduct a simulation to estimate the percentage of dog owners among U.S. households. Assume that you will look at 10 households at a time.
   
   95911 55241 74053 41002 18096 23370
   19411 15586 98282 81306 73024 33198
   03846 22199 73312 59593 05126 99863

Answer 1

The probability that a randomly selected US household own a dog is 0.52

We select a sample of 10 US households and count how many of them have a dog. To simulate this we use the following steps

Since 0.52 is a 2 digit number when we express it in terms of percentages, we will pick a starting location in the random digit table and pick 2 digits at a time. We can either move down the columns or move across the rows to pick the next 2 digit. For example, we can pick the first row+column as our starting location. The first 2 digits that we read would be 95. The next 2 could be 19 (if we move down) or 91 (if we move across)

1. Pick 2 digits from the random digit table, starting at some row/column.
2. If the random number picked is less than 52, then we will mark the family as a dog owner, else we will mark it as not a dog owner
3. Repeat the steps 1,2 10 times and count the number of dog owner families. This is one trial of the simulation.
4. Now repeat the steps 1 through 3, multiple times (say 1000 times) and get 1000 estimates of the number of families with at least one dog.
5. Get an average of these 1000 values and we get the average number of families with the at least one dog
6. If we divide the above average by 10, then we get an estimate of the proportion  of dog owners among U.S. households

Just as a example we will pick the first sample of 10

The numbers are 95,19,03,91,41,84,15,11,62,52. Of these 5 (19,03,,41,15,11) are less than 52 and these are the dog owners. Hence in this simulated sample of 10 families, 5 are dog owners.

We then repeat this 999 more times and get an average value of the dog owning families. Divide this by 10 and we get an estimate of the proportion.