In a poll of 800 high school students, it was found that 25 % have a car. There is a margin of error of 3%. find the following from the above scenario. Write the answers in detail: population, sample, raw data, sample statistics, population parameters

Sure, let's break down the problem and identify the different components:

1. **Population**: 
   The population in this scenario refers to the entire group of high school students that the poll aims to understand. This would be all high school students in the specific area or group being studied, which could be a specific school, district, or another defined group. The exact number of students in the population isn't provided, but it's understood to be larger than the sample size.

2. **Sample**:
   The sample consists of the 800 high school students who were actually surveyed. This group is a subset of the population and is used to make inferences about the larger group.

3. **Raw Data**:
   The raw data in this context would be the individual responses from each of the 800 students in the sample. Specifically, it would be the data on whether each student has a car or not. This could be represented as a list of 800 entries, each marked "yes" or "no".

4. **Sample Statistics**:
   The sample statistics are numerical values that summarize the sample data. In this scenario, the key sample statistic is the percentage of students in the sample who have a car, which is 25%. Additionally, the margin of error provided for this sample statistic is 3%.

   - **Sample proportion (p̂)**: 25% or 0.25
   - **Margin of error (E)**: 3% or 0.03

5. **Population Parameters**:
   The population parameters are the numerical values that summarize the entire population's characteristics. These are usually unknown and are estimated using the sample statistics. In this scenario, the population parameter of interest is the true proportion of all high school students who have a car. The margin of error helps to create a confidence interval for this population parameter.

   - **Population proportion (p)**: Unknown, but estimated to be around 25% based on the sample.
   - **Confidence interval**: Using the margin of error, we can say that we are fairly confident that the true proportion of high school students with a car lies between 22% and 28% (25% ± 3%).

### Detailed Answers

1. **Population**: All high school students in the defined group being studied (e.g., a school, district, or other area).
2. **Sample**: 800 high school students surveyed.
3. **Raw Data**: Individual responses of the 800 students, indicating whether they have a car or not.
4. **Sample Statistics**: 25% of the sample have a car, with a margin of error of 3%.
5. **Population Parameters**: The true proportion of high school students with a car, estimated to be between 22% and 28%.

Would you like further details or have any questions about this analysis? Here are some related questions you might be interested in:

1. How do we calculate the margin of error in a poll?
2. What is the difference between a population parameter and a sample statistic?
3. How do we determine the confidence interval for a population proportion?
4. What are the implications of having a larger or smaller sample size on the margin of error?
5. How can sampling bias affect the results of a poll?

**Tip:** When interpreting poll results, always consider the margin of error and confidence interval to understand the range within which the true population parameter likely falls.

Explore the analysis of a poll conducted among 800 high school students, revealing that 25% own a car with a margin of error of 3%. This webpage discusses key statistical concepts such as population, sample, raw data, sample statistics, and population parameters, along with their implications. Ideal for high school statistics students.

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