Determine whether the value is a parameter or statistic:

a) 20% of vehicles sold are compact cars. 
b) 61.4% of all registered voters turned out for the 2016 elections. 
c) A hospital recently surveyed all their patients and found that 85% were satisfied with their level of care. 
d) Facebook tested the mean amount of time its users use the site each day, and they found the mean amount of time all users use the site is 80 minutes each day. 

To determine whether each value is a **parameter** or a **statistic**, we need to understand the distinction:

- **Parameter**: A parameter is a numerical value that describes a characteristic of a **population**. It is typically fixed and not subject to change, as it refers to an entire group.
- **Statistic**: A statistic is a numerical value that describes a characteristic of a **sample**. It is derived from a subset of the population and can vary depending on the sample chosen.

Now, let's analyze each statement:

### a) 20% of vehicles sold are compact cars.
- This is describing the proportion of compact cars **sold**. If this value refers to all vehicles sold (the entire population of vehicles), then it would be a **parameter**. However, if it's based on a survey or sample of vehicles sold, it would be a **statistic**.
  - **Answer**: **Possibly a parameter** (if referring to all vehicles sold) or **statistic** (if based on a sample).

### b) 61.4% of all registered voters turned out for the 2016 elections.
- This refers to the turnout for the **entire** population of registered voters in the 2016 election. As it describes a characteristic of the **entire population**, this is a **parameter**.
  - **Answer**: **Parameter**.

### c) A hospital recently surveyed all their patients and found that 85% were satisfied with their level of care.
- The statement specifies that the survey involved **all** the patients in the hospital. This means it describes a characteristic of the **population** of patients, so it is a **parameter**.
  - **Answer**: **Parameter**.

### d) Facebook tested the mean amount of time its users use the site each day, and they found the mean amount of time all users use the site is 80 minutes each day.
- This refers to the **mean time of all users** (the entire population of users). Since it describes the characteristic of the **population**, it is a **parameter**.
  - **Answer**: **Parameter**.

### Summary:
- a) **Possibly a parameter** or **statistic** (depends on context)
- b) **Parameter**
- c) **Parameter**
- d) **Parameter**

---

Would you like more details or clarification on any of these points? Here are five related questions to explore further:

1. What is the difference between a sample and a population in statistics?
2. How does sampling affect the interpretation of statistics versus parameters?
3. Can a statistic ever be exactly equal to a parameter? Under what circumstances?
4. How would the interpretation change if the 20% of vehicles sold were based on a sample of vehicles, rather than all vehicles sold?
5. How do we use confidence intervals to estimate parameters from statistics?

**Tip:** Remember, a **parameter** always refers to the whole population, while a **statistic** is based on a sample, so context is crucial in determining whether a value is a parameter or a statistic.

Determine whether the value is a parameter or statistic:

a) 20% of vehicles sold are compact cars.
b) 61.4% of all registered voters turned out for the 2016 elections.
c) A hospital recently surveyed all their patients and found that 85% were satisfied with their level of care.
d) Facebook tested the mean amount of time its users use the site each day, and they found the mean amount of time all users use the site is 80 minutes each day.

Learn how to distinguish between parameters and statistics with real-life examples. This guide explores whether various data points, such as 20% of vehicles sold being compact cars and 61.4% voter turnout, represent a parameter or statistic. Suitable for students in Grades 8-12 studying basic statistics.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation