
2. Approximately 34 percent of U.S. households own at least one cat.
A. Using the random digit table provided below, explain how you would
conduct a simulation to estimate the percentage of cat owners among U.S. households. Assume that you will look at 10 households at a time. (8 points)
95911 55241 74053 41002 18096 23370 19411 15586 98282 81306 73024 33198 03846 22199 73312 59593 05126 99863

### Simulation to Estimate the Percentage of Cat Owners Among U.S. Households:

The goal is to use the given random digit table to simulate a sample of 10 households at a time and estimate the percentage of cat owners based on the known information that approximately 34% of U.S. households own at least one cat.

Here are the steps for the simulation:

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**Step 1: Define the Simulation Parameters**
- 34% of households own cats. This translates to 34 out of 100 households.
- We will assign a range of random digits to represent households with and without cats:
  - Let digits 00–33 represent households that own cats (34% of the total).
  - Let digits 34–99 represent households that do not own cats (66% of the total).

**Step 2: Set the Sample Size**
- You will look at 10 households at a time to simulate.
  
**Step 3: Use the Random Digit Table**
- Start reading the random digit table from left to right, selecting two-digit numbers for each household.

**Step 4: Record Results**
- For each selected two-digit number, check whether it falls in the range 00–33 (household owns a cat) or 34–99 (household does not own a cat).
- Repeat this for 10 households and count how many of those households fall in the 00–33 range (i.e., cat owners).

**Step 5: Estimate the Percentage of Cat Owners**
- After simulating 10 households, calculate the percentage of those 10 households that own a cat. 
- You can repeat this process multiple times (e.g., several groups of 10 households) to get a better estimate.

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### Example Using the Given Random Digit Table

Let’s use the first 10 households from the provided random digit table to perform the simulation:

**Random digits:**  
95911 55241 74053 41002 18096 23370 19411 15586 98282 81306

**First 10 two-digit numbers** (reading two digits at a time):
- 95, 91, 55, 24, 17, 40, 18, 09, 15, 23

Now, compare each number to the range:
- 95: no cat
- 91: no cat
- 55: no cat
- 24: cat owner
- 17: cat owner
- 40: no cat
- 18: cat owner
- 09: cat owner
- 15: cat owner
- 23: cat owner

**Result:**
- Out of 10 households, 6 are cat owners (numbers 24, 17, 18, 09, 15, and 23).

**Percentage of cat owners in this sample:**  
\(\frac{6}{10} \times 100 = 60\%\)

In this case, the estimate of cat ownership in this simulation is 60%. To improve the accuracy, you would repeat the process with different sets of 10 households from the random digit table.

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Would you like further details or explanations?  
Here are five related questions to deepen your understanding:

1. How would increasing the sample size affect the accuracy of the simulation?
2. What would happen if the percentage of cat ownership was different, say 50%?
3. How could you modify the simulation to include households that own more than one cat?
4. Why is it important to use a random digit table for simulations like this?
5. How could you calculate an expected average after running several simulations?

**Tip:** The more samples you use in simulations, the more reliable your estimate will be due to the Law of Large Numbers.

Approximately 34 percent of U.S. households own at least one cat. Using the random digit table provided below, explain how you would conduct a simulation to estimate the percentage of cat owners among U.S. households. Assume that you will look at 10 households at a time.

Learn how to conduct a simulation to estimate the percentage of U.S. households that own cats, using random digit tables and probability concepts. This example demonstrates how to simulate samples of 10 households at a time to determine cat ownership, based on known probabilities.

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