Problem 1 - Algebra 2

Question

For each sample, find the sample proportion. Write it as a percent. 837 out of 1150 insurance applicants have no citations on their driving record.

Step-by-Step Solution

Answer

The sample proportion is approximately 72.7%

Step 1: Identify the variables

The 'successes' in this case are the 837 applicants who have no citations on their driving record, out of a total sample size of 1150 applicants.

Step 2: Calculate the Sample Proportion

Apply the formula for sample proportion which is \( p = \frac{x}{n} \) where p represents the sample proportion, x represents 'successes', and n represents total number of observations. So, plug the given numbers into the formula \( p = \frac{837}{1150} \)

Step 3: Convert to Percentage

Multiply the proportion by 100 and add the percent symbol to convert the proportion to percentage. i.e., \( p \% = p * 100 \% \)

Key Concepts

Understanding Statistics

Statistics is a fascinating field that involves collecting, analyzing, and interpreting data. When we talk about statistics, we are often referring to a system for summarizing data so we can understand what is going on in a particular situation. In our context, we have a group of insurance applicants, and we're interested in the proportion of those who have no citations on their driving record. This is a classic example of what statisticians call a "sample," where a subset of a population is being studied to make inferences about the whole population. When calculating statistics, particularly something like a sample proportion, it helps us understand trends and patterns. This knowledge can then be applied to make informed decisions, like adjusting insurance rates or investigating further into the driving habits of applicants.

Converting Proportions into Percentages

Percentages are an incredibly useful way of expressing proportions because they make comparisons easier to understand and communicate. When you calculate a sample proportion, it is often expressed as a decimal. For example, if you find that the sample proportion of applicants with no citations is approximately 0.7278, it's easier to understand when expressed as a percentage. The process involves multiplying the decimal proportion by 100. So in our case, you would do 0.7278 times 100, which gives you 72.78%. Using percentages is a common practice in data analysis because:

• They are more intuitive for the general public.
• They allow for easy comparison between different samples or populations.
• They simplify complex statistics into more comprehensible figures.

This way, the meaning behind numbers is conveyed more effectively.

Basics of Data Analysis

Data Analysis is all about examining datasets to draw conclusions about the information they contain. This involves several stages, starting from collecting data, cleaning it, processing it, and then interpreting the results. In the example of insurance applicants, we begin with the basic data we collected, which is the number of applicants with no citations. By calculating the sample proportion, we have processed this data from raw numbers into something meaningful. Key steps in data analysis include:

• **Data Collection**: Gathering necessary data or information.
• **Data Cleaning**: Removing any errors or inconsistencies present in the data.
• **Data Processing**: Applying formulas and methods to refine the data, like calculating proportions.
• **Data Interpretation**: Using the results to make informed decisions or conclusions.

With data analysis, understanding complex datasets becomes manageable, enabling us to make evidence-based decisions.