Studyfin
✨ Sign up free
Hey there! Have you ever wondered why a paycheck is sometimes smaller than expected? Let's explore how taxes work!
When you work a job, you earn a starting amount of money. This is called your gross pay. It is the total amount of money you make before any taxes are taken out.
Before you get paid, the government takes a small portion of your earnings. This is called income tax. We can use data from a small group of workers to see how this affects everyone.
After taxes are subtracted, the money left over is your net pay. This is your actual take-home pay. We can analyze a random sample of local workers to estimate the average take-home pay for the whole town.
A researcher surveys a random sample of 10 workers in a small town. She finds that 8 of them pay exactly 15% of their gross pay in income taxes. If the town has 500 workers in total, how many can we infer pay this same tax rate?
- Identify the sample size and the successful matches. Here, 8 out of 10 workers pay a 15% tax rate.
- Write this sample data as a fraction: 8/10.
- Simplify the fraction if needed, or convert it to a decimal. 8/10 is equal to 0.80 or 80%.
- Multiply this fraction by the total population of the town to make an inference. The total population is 500.
- Calculate: (8 / 10) * 500 = 8 * 50 = 400.
- Conclude that we can infer about 400 workers in the town pay a 15% tax rate.
